Chaotic phenomena
DOI10.1007/BF02469299zbMath0586.92002OpenAlexW3190201959WikidataQ52678698 ScholiaQ52678698MaRDI QIDQ1072465
Peter E. Kloeden, Alistair I. Mees
Publication date: 1985
Published in: Bulletin of Mathematical Biology (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02469299
measuresentropychaosdimensionslogistic mapchaotic systemsvan der Pol oscillatorHénon equationLorentz equationshorseshoe mapBaker's transformation
Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) General biology and biomathematics (92B05) Stability theory for ordinary differential equations (34D99) Difference equations (39Axx) Qualitative properties of solutions to partial differential equations (35B99)
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Cites Work
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- Chaos and bifurcation phenomena in limiting central difference scheme
- Homoclinic bifurcations and the area-conserving Henon mapping
- Sur l'itération des polynômes réels quadratiques
- The dynamics of recurrent inhibition
- Cayley's problem and Julia sets
- Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
- Chaos in a three-dimensional single loop feedback system with a piecewise linear feedback function
- A two-dimensional mapping with a strange attractor
- Iterates of maps on an interval
- Asymptotic analysis of the Navier-Stokes equations
- Determining Lyapunov exponents from a time series
- Dimensions and entropies of strange attractors from a fluctuating dynamics approach
- Local and global behavior near homoclinic orbits
- Measuring the strangeness of strange attractors
- Ergodicity and exactness of the shift on C[0,\(\infty)\) and the semiflow of a first-order partial differential equation
- How chaotic is chaos? Chaotic and other noisy dynamics in the frequency domain
- Sensitive dependence to initial conditions for one dimensional maps
- Recurrences and discrete dynamic systems
- Phase locking, period doubling bifurcations and chaos in a mathematical model of a periodically driven oscillator: A theory for the entrainment of biological oscillators and the generation of cardiac dysrhythmias
- Negatively invariant sets of compact maps and an extension of a theorem of Cartwright
- A theorem of Sarkovskii on the existence of periodic orbits of continuous endomorphisms of the real line
- Spatiotemporal patterns in epileptic seizures
- The dynamics of density dependent population models
- Snap-back repellers imply chaos in \(\mathbb{R}^n\)
- On the appearance of chaos in a model of the Belousov reaction
- Periodic metabolic systems: Oscillations in multiple-loop negative feedback biochemical control networks
- Structural stability of nonchaotic difference equations
- The Lorenz equations: bifurcations, chaos, and strange attractors
- Approximate solution of a class of operator equations
- Quantitative universality for a class of nonlinear transformations
- Asymptotic properties of sequences of iterates of nonlinear transformations
- On the nature of turbulence
- The Danziger-Elmergreen theory of periodic catatonic schizophrenia
- Period-Doubling Bifurcations and Associated Universal Properties Including Parameter Dependence
- Stable and chaotic solutions of a first order partial differential equation
- Notes on chaos in the cell population partial differential equation
- Analysis of Newton’s Method at Irregular Singularities
- Newton's Method and Symbolic Dynamics
- Chaotic Difference Equations: Generic Aspects
- Newton's Method, Circle Maps, and Chaotic Motion
- Entropy, Lyapunov exponents, and Hausdorff dimension in differentiable dynamical systems
- The dynamical systems approach to differential equations
- Attractors of partial differential evolution equations and estimates of their dimension
- Are chaotic functions really chaotic
- The unstable separatrix of Feigenbaum's fixed-point
- Roads to turbulence in dissipative dynamical systems
- Discrete Dynamical Systems in Dimensions One and Two
- Chaos and Arnold diffusion in dynamical systems
- Dimension estimates for attractors
- An Interesting Cantor Set
- The topological conjugacy problem for generalized Hénon mappings: some negative results
- Homoclinic and heteroclinic orbits in the double scroll attractor
- A generalization of a theorem of marotto
- Recurrent motions in certain continuum dynamical systems
- Qualitative analysis of the periodically forced relaxation oscillations
- Periodic Points of Continuous Functions
- Homoclinic solution and chaos in
- Stability of Periodic Orbits in the Theorem of Sarkovskii
- On Sharkovsky's cycle coexistence ordering
- Differentiable dynamical systems and the problem of turbulence
- A computer-assisted proof of the Feigenbaum conjectures
- Chaotic motion in nonlinear feedback systems
- Chaotic difference equations are dense
- Period Three Implies Chaos
- Nonlinear double-diffusive convection
- Homoclinic Points of Mappings of the Interval
- Hypergraphic Functions and Bifurcations in Recurrence Relations
- Stable Orbits and Bifurcation of Maps of the Interval
- Bursting Phenomena in Excitable Membranes
- Deterministic Nonperiodic Flow
- Oscillation and Chaos in Physiological Control Systems
- Simple mathematical models with very complicated dynamics
- Almost Periodic Flows and Solutions of Differential Equations
- Differentiable dynamical systems
- On Non-Linear Differential Equations of the Second Order: I. the Equation y¨ − k (1-y 2 )y˙ + y = b λk cos(λl + α), k Large
- A second order differential equation with singular solutions
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