Bifurcation and chaotic behavior in the Euler method for a Kaplan-Yorke prototype delay model

DOI10.1016/S0960-0779(03)00408-9zbMath1048.37030MaRDI QIDQ1878068

Ming-Shu Peng

Publication date: 19 August 2004

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Complex (chaotic) behavior of solutions to functional-differential equations (34K23)

Related Items

The use of the Euler method in identification of multiple bifurcations and chaotic behavior in numerical approximation of delay-differential equations ⋮ A new technique to generate independent periodic attractors in the state space of nonlinear dynamic systems ⋮ Stability and Neimark-Sacker bifurcation of numerical discretization of delay differential equations ⋮ SYNCHRONIZATION AND DESYNCHRONIZATION IN A DELAYED DISCRETE NEURAL NETWORK ⋮ Complex dynamics in discrete delayed models with \(\mathbb D _4\) symmetry ⋮ STABILITY, SYMMETRY-BREAKING BIFURCATIONS AND CHAOS IN DISCRETE DELAYED MODELS ⋮ Symmetry breaking, bifurcations, periodicity and chaos in the Euler method for a class of delay differential equations ⋮ Effective approaches to explore rich dynamics of delay-differential equations ⋮ Higher-codimension bifurcations in a discrete unidirectional neural network model with delayed feedback ⋮ Generating chaotic attractors on a surface ⋮ On the synchronization of delay discrete models ⋮ RICH OSCILLATION PATTERNS IN A SIMPLE DISCRETE-TIME DELAYED NEURON NETWORK AND ITS LINEAR CONTROL

Cites Work

• A prototype model for chaos studies
• Smooth bifurcation of symmetric periodic solutions of functional differential equations
• Ordinary differential equations which yield periodic solutions of differential delay equations
• A note on difference-delay equations
• Uniqueness and nonuniqueness of periodic solutions of x'(t)= -g(x(t-1))
• The asymptotic stability of \(x_{n+1}-ax_ n+bx_{n-k}=0\)
• On the chaotic behaviour of a prototype delayed dynamical system.
• Bifurcation and chaotic behavior in the Euler method for a Uçar prototype delay model
• The stability of special symmetric solutions of with small amplitudes
• THE GENERALIZED HÉNON MAPS: EXAMPLES FOR HIGHER-DIMENSIONAL CHAOS
• Unnamed Item
• Unnamed Item
• Unnamed Item