Analysis, Synchronization, and Robotic Application of a Modified Hyperjerk Chaotic System

Abstract

In this work, a novel hyperjerk system, with hyperbolic sine function as the only nonlinear term, is proposed, as a modification of a hyperjerk system proposed by Leutcho et al. First, a dynamical analysis on the system is performed and interesting phenomena concerning chaos theory, such as route to chaos, antimonotonicity, crisis, and coexisting attractors, are studied. For this reason, the system’s bifurcation diagrams with respect to different parameter values are plotted and its Lyapunov exponents are computed. Afterwards, the synchronization of the system is considered, using active control. The proposed system is then applied, as a chaotic generator, to the problem of chaotic path planning, using a combination of sampling and a modulo tactic technique.

Analysis of a new chaotic system, electronic realization and use in navigation of differential drive mobile robot

“…For example, precedence could be given to a sensory response corresponding to no-motion when a chaotic command signal would navigate the robot out of the workspace, cf. [64].…”

Generation of multi-scrolls in corona virus disease 2019 (COVID-19) chaotic system and its impact on the zero-covid policy

“…The degree of chaos and unpredictability in a system is determined by its sensitivity to the initial conditions, the bifurcation parameter, and the dense oscillatory solutions. The aforementioned features of chaos in continuous systems are increasing its appeal by using it as a transmitter in secure communication 1 , path planing problems 2 – 4 , cryptography 5 and motion control 6 but apart from these applications in engineering, the term ”chaos” continues to be associated with negative impact in biological models and still remain as a villain such as Cancer 7 , Ebola 8 , 9 , Influenza 10 , 11 , HIV 12 , 13 and Parkinson 14 epidemic diseases models.…”

Synchronization of a New Chaotic System Using Adaptive Control: Design and Experimental Implementation

“…From that moment on, several applications associated with chaotic systems have emerged. Some of those are in the areas of neurosystems [6,7], chemical reactions [8,9], secure communications [10][11][12][13][14][15][16][17][18], turbines [19,20], robotics [21][22][23][24], cryptosystems [25][26][27][28][29], medicine [30][31][32][33], lasers [25,34], among others.…”