Complex dynamics of a forced discretized version of the Mackey-Glass delay differential equation

Ahmed Elhassanein

doi:10.3934/dcdsb.2015.20.93

Article Contents

2015, Volume 20, Issue 1: 93-105. Doi: 10.3934/dcdsb.2015.20.93

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Complex dynamics of a forced discretized version of the Mackey-Glass delay differential equation

Ahmed Elhassanein^1,

1.
Math. Dept., Faculty of Science, Damanhour University, Damanhour

Received: May 31, 2013

Revised: March 31, 2014

Published: December 2014

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Abstract

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.

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Mathematics Subject Classification: 37M10, 37N25, 37H10, 37F10, 37G35.

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