The use of the Euler method in identification of multiple bifurcations and chaotic behavior in numerical approximation of delay-differential equations

DOI10.1016/j.chaos.2003.12.044zbMath1054.65126OpenAlexW2095556956MaRDI QIDQ1878263

Ahmet Uçar, Ming-Shu Peng

Publication date: 19 August 2004

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

Full work available at URL: https://doi.org/10.1016/j.chaos.2003.12.044

zbMATH Keywords

limit cyclesperiodic oscillationsquasiperiodic solutionsfinite-dimensional discrete dynamical system

Mathematics Subject Classification ID

Related Items (17)

Chaos in a single-species discrete population model with stage structure and birth pulses ⋮ A new technique to generate independent periodic attractors in the state space of nonlinear dynamic systems ⋮ Complex dynamic behavior in a viral model with delayed immune response ⋮ Stability and Neimark-Sacker bifurcation of numerical discretization of delay differential equations ⋮ Chaos in a discrete delay population model ⋮ Chaotic behavior in a class of delay difference equations ⋮ Stability and bifurcation of a two-dimension discrete neural network model with multi-delays ⋮ Periodic solutions and bifurcations of delay-differential equations ⋮ STABILITY, SYMMETRY-BREAKING BIFURCATIONS AND CHAOS IN DISCRETE DELAYED MODELS ⋮ Existence and convergence of Neimark–Sacker bifurcation for delay differential equations using Runge–Kutta methods ⋮ Stability and bifurcation of numerical discretization of a second-order delay differential equation with negative feedback ⋮ Rich dynamics of discrete delay ecological 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 ⋮ Generating chaotic attractors on a surface ⋮ STEADY STATE SYMMETRY BREAKING IN PERIODICALLY EXCITED SYSTEMS INVOLVING TIME DELAY BY HARMONIC HOMOTOPY ⋮ Stability and bifurcation of a discrete red blood cell survival model

Uses Software

• Matlab

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Uçar prototype model
• A prototype model for chaos studies
• Delay differential equations: with applications in population dynamics
• Smooth bifurcation of symmetric periodic solutions of functional differential equations
• Stability of functional differential equations
• Effective computation of periodic orbits and bifurcation diagrams in delay equations
• Ordinary differential equations which yield periodic solutions of differential delay equations
• A note on difference-delay equations
• Naimark-Sacker bifurcations in the Euler method for a delay differential equation
• The asymptotic stability of \(x_{n+1}-ax_ n+bx_{n-k}=0\)
• Periodic orbits of delay differential equations under discretization
• On the chaotic behaviour of a prototype delayed dynamical system.
• Periodic orbits in the Euler method for a class of delay differential equations.
• Bifurcation and chaotic behavior in the Euler method for a Uçar prototype delay model
• Bifurcation and chaotic behavior in the Euler method for a Kaplan-Yorke prototype delay model
• Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation
• The use of boundary locus plots in the identification of bifurcation points in numerical approximation of delay differential equations
• The stability of special symmetric solutions of with small amplitudes
• Cellular neural networks with non-linear and delay-type template elements and non-uniform grids
• On time-delayed feedback control of chaotic systems
• Oscillation and Chaos in Physiological Control Systems
• THE GENERALIZED HÉNON MAPS: EXAMPLES FOR HIGHER-DIMENSIONAL CHAOS

This page was built for publication: The use of the Euler method in identification of multiple bifurcations and chaotic behavior in numerical approximation of delay-differential equations