Transversal homoclinic orbits in a transiently chaotic neural network

DOI10.1063/1.1488895zbMath1080.37611OpenAlexW2039989652WikidataQ52015572 ScholiaQ52015572MaRDI QIDQ5706317

Shyan-Shiou Chen, Chih-Wen Shih

Publication date: 7 November 2005

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/8bc1bcfbf483d10a6a16f2adf88a9337d6b344e7

Mathematics Subject Classification ID

Dynamical systems in biology (37N25) Neural networks for/in biological studies, artificial life and related topics (92B20) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Related Items (12)

Dynamics and bifurcations of a discrete time neural network with self connection ⋮ Global consensus for discrete-time competitive systems ⋮ Snapback repellers and homoclinic orbits for multi-dimensional maps ⋮ The snapback repellers for chaos in multi-dimensional maps ⋮ Analysis of Snapback Repellers Using Methods of Symbolic Computation ⋮ Chaos induced by regular snap-back repellers ⋮ DYNAMICS FOR DISCRETE-TIME CELLULAR NEURAL NETWORKS ⋮ COEXISTENCE OF MULTISTABILITY AND CHAOS IN A RING OF DISCRETE NEURAL NETWORK WITH DELAYS ⋮ Transiently chaotic neural networks with piecewise linear output functions ⋮ Complex and chaotic dynamics in a discrete-time-delayed Hopfield neural network with ring architecture ⋮ Chaotic dynamics of a delayed discrete-time Hopfield network of two nonidentical neurons with no self-connections ⋮ Delayed transiently chaotic neural networks and their application

Cites Work

• Chaotic behavior in the Henon mapping
• Perturbations of stable and chaotic difference equations
• Snap-back repellers imply chaos in \(\mathbb{R}^n\)
• Chaos and asymptotical stability in discrete-time neural networks
• Stability of skew dynamical systems
• Absolute stability of global pattern formation and parallel memory storage by competitive neural networks
• Period Three Implies Chaos
• Global searching ability of chaotic neural networks
• Snapback repellers as a cause of chaotic vibration of the wave equation with a van der Pol boundary condition and energy injection at the middle of the span
• Neurons with graded response have collective computational properties like those of two-state neurons.
• Cycle-symmetric matrices and convergent neural networks

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