A novel four-step feedback procedure for rapid control of chaotic behavior of the logistic map and unstable traffic on the road

Abstract

We present a new four-step feedback procedure to study the full dynamics of a nonlinear dynamical system, namely, the logistic map. We show that by using this procedure, the chaotic behavior of the logistic map can be controlled easily and rapidly or the system can be made stable for higher values of the population growth parameter. We utilize various dynamical techniques (orbit evolution, time series analysis, bifurcation diagrams, and Lyapunov exponents) to analyze the dynamics of the logistic map. Additionally, we adopt the switching strategy to control chaos or to increase the stability performance of the logistic map. Finally, we propose a modified traffic control model to enable rapid control of unexpected traffic on the road. The results of this model are supported by a physical interpretation. The model is found to be more efficient than existing models of Lo and Cho [J. Franklin Inst. 342, 839-851 (2005)] and Ashish et al. [Nonlinear Dyn. 94, 959-975 (2018)]. This work provides a novel feedback procedure that facilitates rapid control of chaotic behavior and increases the range of stability of dynamical systems.