Discrete superior dynamics of a generalized chaotic system

Abstract

In the past few decades, the discrete dynamics of difference maps have attained the remarkable attention of researchers owing to their incredible applications in different domains, like cryptography, secure communications, weather forecasting, traffic flow models, neural network models, and population biology. In this article, a generalized chaotic system is proposed, and superior dynamics is disclosed through fixed point analysis, time-series evolution, cobweb representation, period-doubling, period-3 window, and Lyapunov exponent properties. The comparative bifurcation and Lyapunov plots report the superior stability and chaos performance of the generalized system. It is interesting to notice that the generalized system exhibits superior dynamics due to an additional control parameter \(\beta \). Analytical and numerical simulations are used to explore the superior dynamical characteristics of the generalized system for some specific values of parameter \(\beta \). Further, it is inferred that the superiority in dynamics of the generalized system may be efficiently used for better future applications.