Bifurcation analysis of a first time-delay chaotic system

Tianzeng Li, Yu Wang, Xiaofeng Zhou
2019 Advances in Difference Equations  
This paper deals with the dynamic behavior of the chaotic nonlinear time delay systems of general formẋ(t) = g(x(t), x(t -τ )). We carry out stability analysis to identify the parameter zone for which the system shows a stable equilibrium response. Through the bifurcation analysis, we establish that the system shows a stable limit cycle through supercritical Hopf bifurcation beyond certain values of delay and parameters. Next, a numerical simulation of the prototype system is used to show that
more » ... he system has different behaviors: stability, periodicity and chaos with the variation of delay and other parameters, which demonstrates the validity of our method. We give the single-and two-parameter bifurcation diagrams which are employed to explore the dynamics of the system over the whole parameter space.
doi:10.1186/s13662-019-2010-y fatcat:iwlivpa6xjaqfc4affkjne5d5i