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Bifurcation and chaotic behavior in the Euler method for a Uçar prototype delay model. (English) Zbl 1061.37022

Summary: A discrete model with a simple cubic nonlinearity term for the symmetric coupling of three fixed-points (one unstable) is treated in the study of bifurcations and chaotic behavior of a prototype delayed dynamical system under discretization. Effective computation of Hopf bifurcations, stable limit cycles (periodic solutions), symmetrical breaking bifurcations and chaotic behavior in nonlinear delayed equations are proposed.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
34K23 Complex (chaotic) behavior of solutions to functional-differential equations
39A12 Discrete version of topics in analysis

Software:

Matlab
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References:

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