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 systems 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.

In this paper, we designed multiple control inputs for Rucklidge oscillator through sliding, adaptive, and backstepping control techniques. Dynamical stability through Lyapunov theory is discussed to check whether the above‐mentioned nonlinear dynamical system is stable or not for defined controller. Based on error dynamics, adaptive and sliding control techniques are used such that solution approaches to its stable state with time. Furthermore, simulation results of nonlinear Rucklidge system are included in this paper to confirm controlled results and to analyze applied techniques. A brief analysis of these techniques for considered dynamical system is an integral part of the paper.