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Complex dynamics of a forced discretized version of the Mackey-Glass delay differential equation. (English) Zbl 1330.37068

Summary: In this paper, the chaotic behaviour of a forced discretized version of the Mackey-Glass delay differential equation is considered for different levels of noise intensity. The existence and stability of the equilibria of the skeleton are studied. The modified straight-line stabilization method is used to control chaos. The autocorrelation structure is discussed. Numerical simulations are employed to show the model’s complex dynamics by means of the largest Lyapunov exponents, bifurcations, time series diagrams and phase portraits. The effects of noise intensity on its dynamics and the intermittency phenomenon are also discussed via simulation.

MSC:

37M10 Time series analysis of dynamical systems
37N25 Dynamical systems in biology
37H10 Generation, random and stochastic difference and differential equations
37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
37G35 Dynamical aspects of attractors and their bifurcations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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