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.
Highlights
Over the last 60 years, chaotic systems have integrated almost every scientific discipline and have found applications in numerous fields, including, but not limited to, biology, engineering, finance, robotics, circuits, cryptography, secure communications, and many more
A novel hyperjerk system is proposed, as a modification of a system proposed by Leutcho et al [10]. e proposed system has only one nonlinear term, yet it yields a plethora of Complexity interesting chaotic phenomena, which are analyzed and discussed, by considering its bifurcation diagrams, spectrum of Lyapunov exponents, and continuation diagrams
For revealing the dynamics of system (2), regarding the value of parameter d, the system’s bifurcation diagram of x versus d has been plotted (Figure 3(a)). e bifurcation diagram is obtained by plotting the variable x when the trajectory cuts the plane y 0 with dy/dt < 0, as the control parameter d increases in very small steps in the range 0.3 ≤ d ≤ 1.4
Summary
Over the last 60 years, chaotic systems have integrated almost every scientific discipline and have found applications in numerous fields, including, but not limited to, biology, engineering, finance, robotics, circuits, cryptography, secure communications, and many more (see, for example, [1,2,3,4,5,6,7,8,9] and the references therein) Due to their deterministic nature and high sensitivity to initial conditions, chaotic systems provide an efficient method of adding complexity and increased security to a design. Extensive simulations are performed to compare the coverage percent and the mean number of visits per cell to the number of movements performed, and the results are discussed. is design scheme showcases one of the many possible applications of the proposed chaotic system in practice
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