Elements of applied bifurcation theory.

DOI10.1007/b98848zbMath0914.58025OpenAlexW4206651839MaRDI QIDQ1269730

Yuri A. Kuznetsov

Publication date: 28 October 1998

Published in: Applied Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/b98848

zbMATH Keywords

numerical methodsequilibriumnormal formbifurcation analysisfinite-dimensional systemgeneric bifurcation

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Normal forms for dynamical systems (37G05) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory (37-01) Local and nonlocal bifurcation theory for dynamical systems (37G99)

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discrete predator-prey model with nonmonotonic functional response, Bifurcation and complex dynamics of a discrete-time predator-prey system with simplified monod-Haldane functional response, Bifurcations and chaos in a discrete predator-prey model with Crowley-Martin functional response, Geometric analysis of oscillations in the Frzilator model, Generalized reproduction numbers, sensitivity analysis and critical immunity levels of an SEQIJR disease model with immunization and varying total population size, Sinusoidal-signal detection by active, noisy oscillators on the brink of self-oscillation, Hopf bifurcation analysis of a diffusive single species model with stage structure and strong Allee effect, Synchronisation vs. resonance: isolated resonances in damped nonlinear oscillators, Hopf and homoclinic bifurcations on the sliding vector field of switching systems in \(\mathbb{R}^3\): a case study in power electronics, On periodic regimes triggered by herd behaviour in population systems, Degenerate grazing-sliding bifurcations in planar Filippov systems, Stability and bifurcation analysis on a discrete-time neural network, Dynamic Hopf bifurcations generated by nonlinear terms, Dynamic analysis of duopoly price game based on low-carbon technology sharing, Simple diffusion can support the pitchfork, the flip bifurcations, and the chaos, Neimark-Sacker bifurcation for periodic delay differential equations, Chaos in a predator-prey-based mathematical model for illicit drug consumption, Regular self-oscillating and chaotic behaviour of a PID controlled gimbal suspension gyro, Hopf bifurcation analysis of the Lü system, Bifurcation, invariant curve and hybrid control in a discrete-time predator-prey system, Stability and bifurcation analysis on a discrete-time system of two neurons., Diversity in interaction strength promotes rich dynamical behaviours in a three-species ecological system, Mate limitation in fungal plant parasites can lead to cyclic epidemics in perennial host populations, Lyapunov coefficients for degenerate Hopf bifurcations and an application in a model of competing populations, Nonhyperbolic periodic orbits of vector fields in the plane revisited, Constructing the second order Poincaré map based on the Hopf-zero unfolding method, Periodic orbits for a three-dimensional biological differential systems, Some applications of Filippov's dynamical systems, Reduction of a model of an excitable cell to a one-dimensional map, Complex dynamics in double-diffusive convection, From global to local bifurcations in a forced Taylor-Couette flow, Some global bifurcations related to the appearance of closed invariant curves, Complex and chaotic dynamics in a discrete-time-delayed Hopfield neural network with ring architecture, Qualitative properties and bifurcations of a leaf-eating herbivores model, Complex oscillatory patterns near singular Hopf bifurcation in a two-timescale ecosystem, Gyrostat model regular and chaotic behavior, Bifurcation analysis and dynamic behaviour of an inverted pendulum with bounded control, Global dynamics of non-smooth Filippov pest-natural enemy system with constant releasing rate, Mathematical studies of the dynamics of finite-size binary neural networks: a review of recent progress, Bifurcation of a feed forward neural network with delay and application in image contrast enhancement, Analysis and simulation of periodic and solitary waves in nonlinear dispersive-dissipative solids, Fractal analysis of planar nilpotent singularities and numerical applications, Flip bifurcation of a discrete predator-prey model with modified Leslie-Gower and Holling-type III schemes, Bifurcation and dynamic analyses of non-monotonic predator-prey system with constant releasing rate of predators, Nominal exchange rate determination and dynamics in an OLG framework, Local bifurcation analysis of one parameter in the Greitzer's model with a general compressor characteristic, On the Lorenz '96 model and some generalizations, Influence of fear effect on bifurcation dynamics of predator-prey system in a predator-poisoned environment, Analysis of the onset of a regime shift and detecting early warning signs of major population changes in a two-trophic three-species predator-prey model with long-term transients, Bifurcation and overexploitation in Rosenzweig-MacArthur model, Nontransversal curves of \(T\)-points: A source of closed curves of global bifurcations, A learning rule with generalized Hebbian synapses, On manifolds of connecting orbits in discretizations of dynamical systems, Endogenous fluctuations under evolutionary pressure in Cournot competition, Dynamical behavior of an epidemic model with a nonlinear incidence rate, LOCAL AND GLOBAL BIFURCATIONS IN THREE-DIMENSIONAL, CONTINUOUS, PIECEWISE SMOOTH MAPS, CONTROLLABLE HOPF BIFURCATIONS OF CODIMENSIONS ONE AND TWO IN LINEAR CONTROL SYSTEMS, PROPER PREDATION MAKES THE SYSTEM DISEASE FREE — CONCLUSION DRAWN FROM AN ECO-EPIDEMIOLOGICAL MODEL, Doubling bifurcation of a closed invariant curve in 3D maps, Subharmonic capillary–gravity waves in large containers subject to horizontal vibrations, A Dynamical System for Prioritizing and Coordinating Motivations, Codimension-3 Flip Bifurcation of a Class of Difference Equations, Stability and Bifurcation of a Class of Stochastic Closed Orbit Equations, Identification of the FitzHugh–Nagumo Model Dynamics via Deterministic Learning, On the stability of some systems of exponential difference equations, Exploring the Dynamics of a Third-Order Phase-Locked Loop Model, Pseudospectral Discretization of Nonlinear Delay Equations: New Prospects for Numerical Bifurcation Analysis, Computer-assisted bifurcation diagram validation and applications in materials science, Forward-Time and Backward-Time Isochrons and Their Interactions, On the Neimark–Sacker bifurcation in a discrete predator–prey system, Dynamics of a parametrically excited simple pendulum, Simplest bifurcation diagrams for monotone families of vector fields on a torus, Crisis of the chaotic attractor of a climate model: a transfer operator approach, Vibration Dynamics of an Inclined Cable Excited Near Its Second Natural Frequency, Evolutionary technology adoption in an oligopoly market with forward-looking firms, Transient chaotic rotating waves in a ring of unidirectionally coupled symmetric Bonhoeffer-van der Pol oscillators near a codimension-two bifurcation point, A “saddle-node” bifurcation scenario for birth or destruction of a Smale–Williams solenoid, Bifurcation analysis and potential landscapes of the p53-Mdm2 module regulated by the co-activator programmed cell death 5, Subcritical Hopf bifurcations in a car-following model with reaction-time delay, Bifurcations in a Seasonally Forced Predator–Prey Model with Generalized Holling Type IV Functional Response, Bursting and Synchronization in a Two-Compartment Model with Current-Feedback Control, Stability and Bifurcation of a Fishery Model with Crowley–Martin Functional Response, DETECTING BOGDANOV–TAKENS BIFURCATION OF TRAVELING WAVES IN REACTION–DIFFUSION SYSTEMS, RESONANCES OF PERIODIC ORBITS IN RÖSSLER SYSTEM IN PRESENCE OF A TRIPLE-ZERO BIFURCATION, ELEMENTAL PERIODIC ORBITS ASSOCIATED WITH THE LIBRATION POINTS IN THE CIRCULAR RESTRICTED 3-BODY PROBLEM, Spatiotemporal Dynamics of the Diffusive Mussel-Algae Model Near Turing-Hopf Bifurcation, Bifurcation analysis and feedback control of a 3D chaotic system, Stability of equilibrium points of demand-inventory model with stock-dependent demand, Bifurcation analysis on a discrete model of Nicholson's blowflies, Bursting Types and Bifurcation Analysis in the Pre-Bötzinger Complex Respiratory Rhythm Neuron, BPS domain walls and vacuum structure of N=1 supergravity coupled to a chiral multiplet, A study of stability and bifurcation analysis in discrete-time predator–prey system involving the Allee effect, Approximated Spiral and Target Patterns in Bazykin’s Prey–Predator Model: Multiscale Perturbation Analysis, Multistable Phenomena Involving Equilibria and Periodic Motions in Predator–Prey Systems, Hopf bifurcation and stability analysis of an predator-prey system with Holling type IV functional response, Naimark-Sacker bifurcation of second order rational difference equation with quadratic terms, Bifurcations and Multistability in a Model of Cytokine-Mediated Autoimmunity, A normal form method for the determination of oscillations characteristics near the primary Hopf bifurcation in bandpass optoelectronic oscillators: Theory and experiment, Qualitative structures of a degenerate fixed point of a Ricker competition model, Current Trends in the Bifurcation Methods of Solutions of Real World Dynamical Systems, Quasi-equilibrium reduction in a general class of stoichiometric producer–consumer models, Bifurcations and dynamics of a discrete predator–prey system, Complex dynamics in biological systems arising from multiple limit cycle bifurcation, Deterministic learning of completely resonant nonlinear wave systems with Dirichlet boundary conditions, On quasiperiodic and subharmonic Floquet wake instabilities, Multiple bifurcations in an early brain tumor model with piecewise constant arguments, Stochasticity induced mixed-mode oscillations and distribution of recurrent outbreaks in an ecosystem, A Generalized 2D-Dynamical Mean-Field Ising Model with a Rich Set of Bifurcations (Inspired and Applied to Financial Crises), Bifurcations of a periodically forced microbial continuous culture model with restrained growth rate, BIFURCATION ANALYSIS OF A DISCRETE-TIME KALDOR MODEL OF BUSINESS CYCLE, On the analysis of the double Hopf bifurcation in machining processes via centre manifold reduction, ON THE NONEQUIVALENCE OF LORENZ SYSTEM AND CHEN SYSTEM, A new risk index, A NOTE ON BIFURCATION CONTROL, LOCAL FEEDBACK CONTROL OF THE NEIMARK–SACKER BIFURCATION, Computation of Periodic Solutions of Conservative Systems with Application to the 3-Body Problem, A Note on Hopf Bifurcation in Chen's System, Baroclinic Flow and the Lorenz-84 Model, One-Parameter Bifurcations in Planar Filippov Systems, BIFURCATIONS IN THE COLPITTS OSCILLATOR: FROM THEORY TO PRACTICE, HOMOCLINIC BRANCH SWITCHING: A NUMERICAL IMPLEMENTATION OF LIN'S METHOD, ACTION AND PERIOD OF HOMOCLINIC AND PERIODIC ORBITS FOR THE UNFOLDING OF A SADDLE-CENTER BIFURCATION, SINGULAR PERTURBATIONS OF QUADRATIC MAPS, QUALITATIVE RESONANCE OF SHIL'NIKOV-LIKE STRANGE ATTRACTORS, PART I: EXPERIMENTAL EVIDENCE, QUALITATIVE RESONANCE OF SHIL'NIKOV-LIKE STRANGE ATTRACTORS, PART II: MATHEMATICAL ANALYSIS, NUMERICAL ANALYSIS OF DEGENERATE CONNECTING ORBITS FOR MAPS, IMPLICIT CRITERIA OF EIGENVALUE ASSIGNMENT AND TRANSVERSALITY FOR BIFURCATION CONTROL IN FOUR-DIMENSIONAL MAPS, THE FOLD-FLIP BIFURCATION, NONLINEAR ANALYSIS OF A NETWORK OF THREE CONTINUOUS STIRRED TANK REACTORS WITH PERIODIC FEED SWITCHING: SYMMETRY AND SYMMETRY-BREAKING, DEGENERATE BIFURCATIONS AND BORDER COLLISIONS IN PIECEWISE SMOOTH 1D AND 2D MAPS, An eigenvalue based approach for the robust stabilization of linear time-delay systems, DEVELOPMENT OF THERAPEUTIC BRAIN STIMULATION TECHNIQUES WITH METHODS FROM NONLINEAR DYNAMICS AND STATISTICAL PHYSICS, Algebraic Analysis of Bifurcation and Limit Cycles for Biological Systems, Turing–Hopf Bifurcation and Spatio-Temporal Patterns of a Ratio-Dependent Holling–Tanner Model with Diffusion, On Uniqueness of Limit Cycles in General Bogdanov–Takens Bifurcation, Fold-Pitchfork Bifurcation, Arnold Tongues and Multiple Chaotic Attractors in a Minimal Network of Three Sigmoidal Neurons, NUMERICAL REVISIT TO A CLASS OF ONE-PREDATOR, TWO-PREY MODELS, DYNAMICAL BEHAVIOR ANALYSIS OF A TWO-DIMENSIONAL DISCRETE PREDATOR-PREY MODEL WITH PREY REFUGE AND FEAR FACTOR, Phase portraits of the quadratic polynomial Liénard differential systems, Hopf-pitchfork bifurcation of coupled van der Pol oscillator with delay, Nonlinear dynamics of fully developed swirling jets, Bifurcation analysis of the flour beetle population growth equations, Bifurcation analysis in a discrete BAM network model with delays, Neimark–Sacker Bifurcation and Stability of a Certain Class of Host-Parasitoid Models with Host Refuge Effect, Detecting coexisting oscillatory patterns in delay coupled Lur’e systems, Synchronization and locking in oscillators with flexible periods, Modelling finger propagation in elasto-rigid channels, Hopf Bifurcation in an Oscillatory-Excitable Reaction–Diffusion Model with Spatial Heterogeneity, Transition in the asymptotic suction boundary layer over a heated plate, A MODIFIED GENERALIZED LORENZ-TYPE SYSTEM AND ITS CANONICAL FORM, Sensitivity Analysis of Limit Cycles in an Alpha Stirling Engine: A Bifurcation-Theory Approach, Spatiotemporal patterns induced by cross-diffusion in predator–prey model with prey herd shape effect, BIFURCATIONS OF A HOLLING-TYPE II PREDATOR–PREY SYSTEM WITH CONSTANT RATE HARVESTING, TWO-DIMENSIONAL BIFURCATION DIAGRAMS OF A CHAOTIC CIRCUIT BASED ON HYSTERESIS, Bifurcation analysis of a periodically forced pair of tubular catalytic combustors, Discretization of conformable fractional differential equations by a piecewise constant approximation, Dynamical response of a reaction–diffusion predator–prey system with cooperative hunting and prey refuge, BUILDING ELECTRONIC BURSTERS WITH THE MORRIS–LECAR NEURON MODEL, Border Collision Bifurcations and Chaos in a Ring of Three Unidirectionally Coupled Nonmonotonic Piecewise Constant Neurons, Unnamed Item, ON THE MULTIPLE SHOOTING CONTINUATION OF PERIODIC ORBITS BY NEWTON–KRYLOV METHODS, Hopf Bifurcation in an Augmented Solow Model with Two Delays, On the analysis of stability, bifurcation, and chaos control of discrete-time predator-prey model with Allee effect on predator, A SURVEY OF METHODS FOR COMPUTING (UN)STABLE MANIFOLDS OF VECTOR FIELDS, NUMERICAL CONTINUATION OF BRANCH POINTS OF EQUILIBRIA AND PERIODIC ORBITS, GLOBAL DYNAMICS OF A PREY–PREDATOR MODEL WITH HOLLING TYPE III FUNCTIONAL RESPONSE IN THE PRESENCE OF HARVESTING, METHODS OF THE QUALITATIVE THEORY FOR THE HINDMARSH–ROSE MODEL: A CASE STUDY – A TUTORIAL, COMPUTATION AND VISUALIZATION OF BIFURCATION SURFACES, BIFURCATIONS, AND TEMPORAL AND SPATIAL PATTERNS OF A MODIFIED LOTKA–VOLTERRA MODEL, Dynamics and bifurcations of laminar annular swirling and non-swirling jets, Continuation-Based Numerical Detection of After-Depolarization and Spike-Adding Thresholds, Dynamics of a predator–prey system with nonlinear prey-taxis, Stability and bifurcation of dynamic contact lines in two dimensions, Bifurcation Analysis of Multiscale Malaria Model with Serratia AS1 Bacteria and Saturated Treatment, Dynamics in a discrete time model of logistic type, The interaction of multiple bubbles in a Hele-Shaw channel, Hopf Bifurcations in a Watt Governor with a Spring, Tumor Control, Elimination, and Escape through a Compartmental Model of Dendritic Cell Therapy for Melanoma, Global organization of three-dimensional, volume-preserving flows: Constraints, degenerate points, and Lagrangian structure, Patterns in a Modified Leslie–Gower Model with Beddington–DeAngelis Functional Response and Nonlocal Prey Competition, Ricocheting inclined layer convection states, Bifurcation Analysis for a Food Chain Model with Nonmonotonic Nutrition Conversion Rate of Predator to Top Predator, Bifurcation Analysis of a Predator–Prey Model with Age Structure, A Review on Multiple Purely Imaginary Spectral Values of Time-Delay Systems, Complex Dynamics of a Discrete-Time Prey–Predator System with Leslie Type: Stability, Bifurcation Analyses and Chaos, Tristable Phenomenon in a Predator–Prey System Arising from Multiple Limit Cycles Bifurcation, Numerical Algorithms for the Parametric Continuation of Stiff ODEs Deriving from the Modeling of Combustion with Detailed Chemical Mechanisms, Operator methods for calculating Lyapunov values in problems on local bifurcations of dynamical systems, Mesoscale symmetries explain dynamical equivalence of food webs, An improvement of the non-existence region for limit cycles of the Bogdanov-Takens system, Unnamed Item, NEIMARK-SACKER BIFURCATION OF A SEMI-DISCRETE HEMATOPOIESIS MODEL, A Surface of Heteroclinic Connections Between Two Saddle Slow Manifolds in the Olsen Model, BIFURCATION ANALYSIS OF AN SIRS EPIDEMIC MODEL WITH STANDARD INCIDENCE RATE AND SATURATED TREATMENT FUNCTION, Qualitative properties and two strong resonances of a discrete reduced Lorenz system, Pattern Storage, Bifurcations, and Groupwise Correlation Structure of an Exactly Solvable Asymmetric Neural Network Model, Detection of Synergistic Combinatorial Perturbations by a Bifurcation-Based Approach, Basin bifurcations, oscillatory instability and rate-induced thresholds for Atlantic meridional overturning circulation in a global oceanic box model, The influence of invariant solutions on the transient behaviour of an air bubble in a Hele-Shaw channel, Controlling chaos and Neimark-Sacker bifurcation in a discrete-time predator-prey system, Developing and studying the dynamical behavior of a nonlinear mathematical model for cancers with tumor by considering immune system role, ZERO BIFURCATION DIAGRAMS FOR ABELIAN INTEGRALS: A STUDY ON HIGHER-ORDER HYPERELLIPTIC HAMILTONIAN SYSTEMS WITH THREE PERTURBATION PARAMETERS, Box dimension of Neimark–Sacker bifurcation, A Definition of Cellular Interface Problems, The Neimark-Sacker bifurcation ofx_n+1=δx_n-2+x_n-3A+x_n-3, Excitability Mediated by Dissipative Solitons in Nonlinear Optical Cavities, On the dynamics of multi-species Ricker models admitting a carrying simplex, Finite-size and correlation-induced effects in Mean-field Dynamics, Bifurcations of a Bouncing Ball Dynamical System, Pattern Analysis in Networks of Diffusively Coupled Lur’e Systems, Time delay in the swing equation: A variety of bifurcations, Bursting patterns and mixed-mode oscillations in reduced Purkinje model, Practical dynamic consensus of Stuart–Landau oscillators over heterogeneous networks, A New Class of Two-Dimensional Chaotic Maps with Closed Curve Fixed Points, Complex Dynamical Behaviors in a 3D Simple Chaotic Flow with 3D Stable or 3D Unstable Manifolds of a Single Equilibrium, Bifurcation analysis and frequency prediction in shear-driven cavity flow, Numerical methods for nonlinear equations, Hopf Bifurcations for Neutral Functional Differential Equations with Infinite Delays, Stability and Hopf bifurcation analysis in a Lotka–Volterra competition–diffusion–advection model with time delay effect ^*, The Lengyel–Epstein Reaction Diffusion System, Stability and Neimark–Sacker bifurcation for a discrete Nicholson's blowflies model with proportional delay, Neimark-Sacker bifurcation analysis in a discrete neutral Nicholson’s blowflies system with delay, Unnamed Item, Experimental observations on unsafe zones in milling processes, Dynamical analysis of tumor-immune-help T cells system, Continuation and stability of rotating waves in the magnetized spherical Couette system: secondary transitions and multistability, Existence and spectral instability of bounded spatially periodic traveling waves for scalar viscous balance laws, Global dynamics of a quintic Liénard system with Z2 -symmetry I: saddle case, Unnamed Item, Hopf bifurcation in a gene regulatory network model: Molecular movement causes oscillations, Comparison of dynamical behavior between fractional order delayed and discrete conformable fractional order tumor-immune system, Qualitative analysis and optimal control of an SIR model with logistic growth, non-monotonic incidence and saturated treatment, Bifurcations of a second-order difference equation related to a class of reaction–diffusion equations, Centers in a Quadratic System Obtained from a Scalar Third Order Differential Equation, Continuation of Bifurcations of Periodic Orbits for Large-Scale Systems, Shilnikov Homoclinic Bifurcation of Mixed-Mode Oscillations, BIFURCATION AND CHAOS IN A DISCRETE PREDATOR–PREY MODEL WITH HOLLING TYPE-III FUNCTIONAL RESPONSE AND HARVESTING EFFECT, Stability properties of periodically driven overdamped pendula and their implications to physics of semiconductor superlattices and Josephson junctions, Noise-Driven Oscillations in Coupled Excitable Systems, Inhomogeneous percolation on multilayer networks, Unnamed Item, Analytic invariant curves for an iterative equation related to mosquito model, Introduction to the Geometric Theory of ODEs with Applications to Chemical Processes, Creation of Neimark-Sacker Bifurcation for a Three-Degree-of-Freedom Vibro-Impact System with Clearances, Application of Mathematical Epidemiology to Crop Vector-Borne Diseases: The Cassava Mosaic Virus Disease Case, Exponential-Algebraic Maps and Chaos in 3D Autonomous Quadratic Systems, A New 6D Hyperchaotic System with Four Positive Lyapunov Exponents Coined, Dynamics of a discrete predator-prey model with Holling-II functional response, On an Invasive Species Model with Harvesting, Chaos and Wild Chaos in Lorenz-Type Systems, Extensional equality preservation and verified generic programming, Peculiarities of the transitions to synchronization in coupled systems with amplitude death, Disease extinction and persistence in a discrete-time sis epidemic model with vaccination and varying population size, Hopf bifurcation for a discontinuous HTLV-1 model, Bifurcation analysis of an e-epidemic model in wireless sensor network, Instability of small-amplitude periodic waves from fold-Hopf bifurcation, BISTABILITY AND TRISTABILITY IN A PREDATOR–PREY MODEL WITH STRONG ALLEE EFFECT IN PREY, Qualitative study of a second order difference equation, Periodic traveling waves with large speed, Spectral instability of small-amplitude periodic waves for hyperbolic non-Fickian diffusion advection models with logistic source, Dynamical complexities of a discrete Ivlev-type predator-prey system, Bifurcation and chaos of a nonlinear discrete-time predator-prey model involving the nonlinear Allee effect, Chaotic dynamics of the fractional order Schnakenberg model and its control, Bifurcation of Limit Cycles from a Fold-Fold Singularity in Planar Switched Systems, A higher-dimensional generalization of the Lozi map: bifurcations and dynamics, Destabilization of a seasonal synchronization in a population model with a seasonally varying Allee effect, Arbitrarily weak head-on collision can induce annihilation: the role of hidden instabilities, Zero-Hopf bifurcation of a memristive synaptic Hopfield neural network with time delay, Balanced‐budget rules: Local indeterminacy and bifurcations, Pollution effects on disease transmission and economic stability, A Quintic \(\boldsymbol{\mathbb{Z}_2}\)-Equivariant Liénard System Arising from the Complex Ginzburg–Landau Equation, BIFURCATION ANALYSIS OF A MODIFIED LESLIE–GOWER PREDATOR–PREY MODEL WITH HUNTING COOPERATION AND FAVORABLE ADDITIONAL FOOD FOR PREDATOR, BIFURCATION ANALYSIS OF AN ALLELOPATHIC PHYTOPLANKTON MODEL, Dynamical behaviors of van der Pol-Duffing systems with indefinite degree, A hierarchical parametric analysis on Hopf bifurcation of an epidemic model, Imperfect and Bogdanov-Takens bifurcations in biological models: from harvesting of species to isolation of infectives, Zero-Hopf bifurcation in the Chua’s circuit, A generically singular type of saddle-node bifurcation that occurs for relativistic shock waves, On solvability of homological equations in the problem of center manifold approximation, Unveiling the dynamics of canard cycles and global behaviour in a singularly perturbed predator-prey system with Allee effect in predator, Dynamical analysis of a two-dimensional discrete predator-prey model, Global Bifurcation Map of the Homogeneous States in the Gray–Scott Model, From Hopf Bifurcation to Limit Cycles Control in Underactuated Mechanical Systems, Bifurcation analysis of macroscopic traffic flow model based on the influence of road conditions., Coupling dynamics of 2D notch-delta signalling, Periodic, nonperiodic, and chaotic solutions for a class of difference equations with negative feedback, Controlling chaos in New Keynesian macroeconomics, An optimisation-based domain-decomposition reduced order model for the incompressible Navier-Stokes equations, Bifurcation analysis in a discrete predator-prey model with herd behaviour and group defense, Strong resonance bifurcations and state feedback control in a discrete prey-predator model with harvesting effect, Wave propagation in one-dimensional nonlinear acoustic metamaterials, An artificial neural network approach to bifurcating phenomena in computational fluid dynamics, Qualitative inverse problems: mapping data to the features of trajectories and parameter values of an ODE model, Multiple bifurcations in a mathematical model of glioma-immune interaction, Torus and homoclinic bifurcations on a cells repair regulations model of the metastatic nasopharyngeal carcinoma, On norm-based estimations for domains of attraction in nonlinear time-delay systems, The Steady State Bifurcation for General Network-Organized Reaction-Diffusion Systems and Its Application in a Metapopulation Epidemic Model, Complicate bifurcation behaviors of a discrete predator–prey model with group defense and nonlinear harvesting in prey, Codimension-2 bifurcation in a discrete predator–prey system with constant yield predator harvesting, Complex dynamics of a discrete-time SIR model with nonlinear incidence and recovery rates, Analytical bifurcation and strong resonances of a discrete Bazykin–Berezovskaya predator–prey model with Allee effect, Stability, bifurcation analysis, and chaos control of a discrete bioeconomic model, Bifurcation patterns in a discrete predator-prey model incorporating ratio-dependent functional response and prey harvesting, Study of co-dimension two bifurcation of a prey-predator model with prey refuge and non-linear harvesting on both species, Hopf bifurcation analysis and existence of heteroclinic orbit and homoclinic orbit in an extended Lorenz system, On the detection of nonlinear normal mode-related isolated branches of periodic solutions for high-dimensional nonlinear mechanical systems with frictionless contact interfaces, Bifurcation of Limit Cycles from Boundary Equilibria in Impacting Hybrid Systems, Dynamical inquest of refuge and bubbling issues in an interacting species system, Catastrophic or sustainable scenarios might occur when the carrying capacities of a tourism‐based socioecological system vary, The analysis of NSG system for existence of Si'lnikov chaos, The Pitchfork Bifurcation, The Real-Valued Maxwell–Bloch Equations with Controls: From a Hamilton–Poisson System to a Chaotic One, Quasiperiodicity and Chaos Through Hopf–Hopf Bifurcation in Minimal Ring Neural Oscillators Due to a Single Shortcut, Unnamed Item, ON THE NUMBER OF LIMIT CYCLES IN PIECEWISE-LINEAR LIÉNARD SYSTEMS, BIFURCATION CONTROL OF A PREDATOR–PREY MODEL BASED ON NUTRITION KINETICS, COMPLEX DYNAMICAL ANALYSIS OF A COUPLED NETWORK FROM INNATE IMMUNE RESPONSES, THE NONEQUIVALENCE AND DIMENSION FORMULA FOR ATTRACTORS OF LORENZ-TYPE SYSTEMS, A STUDY OF THE COEXISTENCE OF THREE TYPES OF ATTRACTORS IN AN AUTONOMOUS SYSTEM, General Method of Construction of Implicit Discrete Maps Generating Chaos in 3D Quadratic Systems of Differential Equations, Dynamical analysis and numerical simulation of a new Lorenz-type chaotic system, Nonresonant Double Hopf Bifurcation in Toxic Phytoplankton–Zooplankton Model with Delay, Polynomial estimates and discrete saddle-node homoclinic orbits, Corner collision implies border-collision bifurcation, Death of period-doublings: Locating the homoclinic-doubling cascade, Bifurcations in a planar system of differential delay equations modeling neural activity, Competition between axisymmetric and three-dimensional patterns between exactly counter-rotating disks, Slow passage through homoclinic orbits for the unfolding of a saddle-center bifurcation and the change in the adiabatic invariant, Empirical assessment of bifurcation regions within New Keynesian models, Deformation of curved BPS domain walls and supersymmetric flows on 2d Kähler-Ricci soliton, Clines in quantitative traits: the role of migration patterns and selection scenarios, A procedure for the computation of accurate PWL approximations of non‐linear dynamical systems, BIFURCATIONS AND LIMIT DYNAMICS IN ADAPTIVE CONTROL SYSTEMS, BORDER COLLISION BIFURCATIONS IN THE EVOLUTION OF MUTUALISTIC INTERACTIONS, TRANSFORMING SUBHARMONIC CHAOS TO HOMOCLINIC CHAOS SUITABLE FOR PATTERN RECOGNITION, TUNING CHAOS SYNCHRONIZATION AND ANTI-SYNCHRONIZATION FOR APPLICATIONS IN TEMPORAL PATTERN RECOGNITION, SYMMETRIC PERIODIC ORBITS AND GLOBAL DYNAMICS OF TORI IN AN O(2) EQUIVARIANT SYSTEM: TWO-DIMENSIONAL THERMAL CONVECTION, RATING THE PERFORMANCE OF SHOOTING METHODS FOR THE COMPUTATION OF PERIODIC ORBITS, Dynamical Systems with a Codimension-One Invariant Manifold: The Unfoldings and Its Bifurcations, Unnamed Item, Spatiotemporal Complexity Analysis for a Space-Time Discrete Generalized Toxic-Phytoplankton-Zooplankton Model with Self-Diffusion and Cross-Diffusion, Controlling Hidden Dynamics and Multistability of a Class of Two-Dimensional Maps via Linear Augmentation, Birth and destruction of collective oscillations in a network of two populations of coupled type 1 neurons, BIFURCATIONS AND CHAOS CONTROL IN A DISCRETE-TIME PREDATOR-PREY SYSTEM OF LESLIE TYPE, Lyapunov Coefficients for Hopf Bifurcations in Systems with Piecewise Smooth Nonlinearity, Bifurcation analysis and chaos control of a second-order exponential difference equation