SLOW–FAST DYNAMICS GENERATED BY NONINVERTIBLE PLANE MAPS

DOI10.1142/S0218127405014192zbMath1096.37022OpenAlexW2025145600MaRDI QIDQ5474362

Andrej L. Shil'nikov, Christian Mira

Publication date: 23 June 2006

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127405014192

zbMATH Keywords

chaotic attractorscanardchaotic transients2D polynomial noninvertible mapstwo time scale dynamics

Mathematics Subject Classification ID

Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Low-dimensional dynamical systems (37E99) Systems with slow and fast motions for nonlinear problems in mechanics (70K70)

Related Items (4)

Noninvertible maps and their embedding into higher dimensional invertible maps ⋮ Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale ⋮ Discretized fast-slow systems with canards in two dimensions ⋮ Boundary-Crisis-Induced Complex Bursting Patterns in a Forced Cubic Map

Cites Work

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• Chaos and fractal properties induced by noninvertibility of models in the form of maps
• Geometric singular perturbation theory for ordinary differential equations
• Subthreshold oscillations in a map-based neuron model
• BASIN BIFURCATIONS OF TWO-DIMENSIONAL NONINVERTIBLE MAPS: FRACTALIZATION OF BASINS
• On Some Properties of Invariant Sets of Two-Dimensional Noninvertible Maps
• ORIGIN OF CHAOS IN A TWO-DIMENSIONAL MAP MODELING SPIKING-BURSTING NEURAL ACTIVITY

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