scientific article

Publication date: 1979

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

snap-back repeller Hausdorff dimension chaos for self maps of n-space dimension of the chaotic set Liapunov characteristic exponents

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Dimension theory in general topology (54F45) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items

Dynamical Taxonomy: Some Taxonomic Ranks to Systematically Classify Every Chaotic Attractor, On nonlinear horizontal dynamics and vibrations control for high-speed elevators, A converse statement to Hutchinson's theorem and a dimension gap for self-affine measures, Dynamical transitions in large systems of mean field-coupled Landau-Stuart oscillators: Extensive chaos and cluster states, Anosov representations with Lipschitz limit set, Predicting turbulent dynamics with the convolutional autoencoder echo state network, Chaos may enhance expressivity in cerebellar granular layer, Harmonic Oscillators with Nonlinear Damping, Stability analysis of chaotic systems from data, Dimension approximation in smooth dynamical systems, Dynamical Analysis of a Three-Dimensional Non-autonomous Chaotic Circuit Based on a Physical Memristor, Generation of Robust Hyperbolic Chaos in CNN, A chaotic model for the epidemic of Ebola virus disease in West Africa (2013–2016), Synchronization of fuzzy-chaotic systems with Z-controller in secure communication, Attractors for Nonautonomous Navier–Stokes System and Other Partial Differential Equations, Dynamics of a Mathematical Hematopoietic Stem-Cell Population Model, Route to hyperbolic hyperchaos in a nonautonomous time-delay system, Generalized redundancies for time series analysis, Existence and finite-dimensionality of attractors for a system of equations arising in ferromagnetism, Effects of stochastic parametrization on extreme value statistics, Power law wave number spectra of fractal particle distributions advected by flowing fluids, Deterministic and stochastic bifurcations in two-dimensional electroconvective flows, Convolutional autoencoder and conditional random fields hybrid for predicting spatial-temporal chaos, Linear response in neuronal networks: From neurons dynamics to collective response, Robust Hyperbolic Chaos in Froude Pendulum with Delayed Feedback and Periodic Braking, Multiscale measures of phase-space trajectories, A New Category of Three-Dimensional Chaotic Flows with Identical Eigenvalues, Cooperative hunting in a discrete predator–prey system, Dynamics of the nonholonomic Suslov problem under periodic control: unbounded speedup and strange attractors, On the complex dynamics of functional-coefficients nonlinear autoregressive time series models, A piecewise-linear invertible noodle map, Regular and chaotic dynamics in the rubber model of a Chaplygin top, A ``superfat chaotic attractor, A data-driven, physics-informed framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings, Dimension estimate of the global attractor for resonant motion of a spherical pendulum, Fractal features of invariant sets in a three-dimensional map, Consistent nonlinear dynamics: identifying model inadequacy, Chaotic behavior in the dynamical system of a continuous stirred tank reactor, Exponential decay of power spectra at high frequency and positive Lyapunov exponents, Theoretical and experimental time series analysis of an inductorless Chua's circuit, An overview of bifurcation, chaos and nonlinear dynamics in control systems, Parametric smoothness and self-scaling of the statistical properties of a minimal climate model: what beyond the mean field theories?, Chaotic thermal convection of couple-stress fluid layer, Bifurcations of the symmetric quasi-periodic motion and Lyapunov dimension of a vibro-impact system, Bistability, bifurcations and chaos in the Mackey-Glass equation, Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations, Dynamic analysis of discrete-time, continuous-time and delayed feedback jerky equations, Nonlinear analysis and minimum \(\mathrm{L}_2\)-norm control in memcapacitor-based hyperchaotic system via online particle swarm optimization, Low-frequency variability and heat transport in a low-order nonlinear coupled ocean-atmosphere model, Chaos in the water resources system, Rich dynamics in some discrete-time car-following models, A new 4-D hyper chaotic system generated from the 3-D Rössler chaotic system, dynamical analysis, chaos stabilization via an optimized linear feedback control, it's fractional order model and chaos synchronization using optimized fractional order sliding mode control, Some historical aspects of nonlinear dynamics -- possible trends for the future, Construction of the Lyapunov spectrum in a chaotic system displaying phase synchronization, Amplitude modulated dynamics and bifurcations in the resonant response of a structure with cyclic symmetry, Analysis of a new quadratic 3D chaotic attractor, Generalized Lorenz equations for acoustic-gravity waves in the atmosphere: attractors dimension, convergence and homoclinic trajectories, On some simple examples of mechanical systems with hyperbolic chaos, Bifurcations and chaos in convection taking non-Fourier heat-flux, Determining Lyapunov spectrum and Lyapunov dimension based on the Poincaré map in a vibro-impact system, Integrability analysis of chaotic and hyperchaotic finance systems, Evaluating Lyapunov exponent spectra with neural networks, Chaos analysis and explicit series solutions to the seasonally forced SIR epidemic model, A family of models with blue sky catastrophes of different classes, The stability cone for a difference matrix equation with two delays, Two nonholonomic chaotic systems. I: On the Suslov problem, Two nonholonomic chaotic systems. II: On the rolling of a nonholonomic bundle of two bodies, Hidden attractor and homoclinic orbit in Lorenz-like system describing convective fluid motion in rotating cavity, Lyapunov exponents and information dimension of the mass distribution in turbulent compressible flows, Exact dimension of Furstenberg measures, Lyapunov dimension formula for the global attractor of the Lorenz system, Fractal dimension estimation with persistent homology: a comparative study, The first 180 Lyapunov exponents for two-dimensional complex Ginzburg-Landau-type equation, A new chaotic attractor from hybrid optical bistable system, Hyperbolic chaos in a system of two Froude pendulums with alternating periodic braking, A continuous planar map with many periodoc points, Spatio-temporal phenomena in complex systems with time delays, Lyapunov exponents for particles advected in compressible random velocity fields at small and large Kubo numbers, Windows and routes to chaos in mixed convection in confined spaces., Dynamic modes of population size and its genetic structure for species with nonoverlapping generations and stage development, Complex dynamics in a harvested nutrient-phytoplankton-zooplankton model with seasonality, Numerical convergence of the Lyapunov spectrum computed using low Mach number solvers, On the gluing and ungluing of strange attractors in the study of the Lorenz system, Nonequilibrium molecular dynamics, fractal phase-space distributions, the Cantor set, and puzzles involving information dimensions for two compressible baker maps, Stability of symbolic embeddings for difference equations and their multidimensional perturbations, On lags and chaos in economic dynamic models, State space reconstruction in the presence of noise, Rich dynamics in some generalized difference equations, Cross frequency coupling in next generation inhibitory neural mass models, Synchronizing the chaotic oscillations by external force, Bifurcation, routes to chaos, and synchronized chaos of electromagnetic valve train in camless engines, Hyperbolic chaos in systems based on Fitzhugh-Nagumo model neurons, Comparing dynamics initiated by an attached oscillating particle for the nonholonomic model of a Chaplygin sleigh and for a model with strong transverse and weak longitudinal viscous friction applied at a fixed point on the body, Self-propulsion of a smooth body in a viscous fluid under periodic oscillations of a rotor and circulation, The self-propulsion of a foil with a sharp edge in a viscous fluid under the action of a periodically oscillating rotor, The wind-driven ocean circulation: applying dynamical systems theory to a climate problem, A 5D hyperchaotic Sprott B system with coexisting hidden attractors, Codimension-two bifurcation, chaos and control in a discrete-time information diffusion model, Bifurcations, chaos and synchronization in ADVP circuit with parallel resistor, Dynamical behavior in the perturbed compound KdV-Burgers equation, Stability analysis, routes to chaos, and quenching chaos in electromechanical valve actuators, The Lyapunov dimension and its estimation via the Leonov method, An autonomous system with attractor of Smale-Williams type with resonance transfer of excitation in a ring array of van der Pol oscillators, On the topology of solenoidal attractors of the cylinder, A comparison of correlation and Lyapunov dimensions, Hopf bifurcations, Lyapunov exponents and control of chaos for a class of centrifugal flywheel governor system, Lyapunov functions in the global analysis of chaotic systems, Can a polynomial interpolation improve on the Kaplan-Yorke dimension?, Experimental distinction between chaotic and strange nonchaotic attractors on the basis of consistency, On determining the dimension of chaotic flows, Bifurcations of tori and phase locking in a dissipative system of differential equations, Chaos and chaos synchronization for a non-autonomous rotational machine systems, Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system, Complex dynamics of a catalytic network having faulty replication into error-species, Dynamics of a discrete-time stage-structured predator-prey system with Holling type II response function, Local Lyapunov exponents of the quasi-geostrophic ocean dynamics, Numerical justification of Leonov conjecture on Lyapunov dimension of Rossler attractor, The dimension spectrum of Axiom A attractors, Two chaotic global models for cereal crops cycles observed from satellite in northern Morocco, Hyperchaos numerical simulation and control in a 4D hyperchaotic system, Complex dynamics in nonlinear triopoly market with different expectations, Nonlinear stiffness, Lyapunov exponents, and attractor dimension, Deep learning of conjugate mappings, \textit{A priori} analysis of reduced description of dynamical systems using approximate inertial manifolds, Estimation of intensive quantities in spatio-temporal systems from time-series, A sudy of back propagation learning with periodic chaos neurons, Critical parameters of the synchronisation's stability for coupled maps in regular graphs, Convergence of a chaotic attractor with increased spatial resolution of the Ginzburg-Landau equation., Chaotic phenomena, Chaotic maps and pattern recognition---the XOR problem