Dynamic Analysis of New Hyperchaotic Hyperjerk System with Infinitely Many Rest Points for Sustainable Energy Applications

The relationship between chaotic systems and sustainable energy is complex but significant. Chaotic systems are governed by deterministic rules, they can be so complex that, even though they don’t involve any randomness or external factors, their future behavior is nearly impossible to predict over long periods, can be found in various aspects of energy production and consumption. A hyperchaotic system is a more complex, higher-dimensional version of a chaotic system, characterized by multiple directions of instability and heightened sensitivity to initial conditions. This complex dynamics of the system can be used to enhance the security of the many communication systems. Hyperjerk system is a new mechanical system. In this article, a new hyperchaotic hyperjerk system is constructed with infinitely many rest points which is the unique feature of the proposed system. The basic properties of the new system such as the nature of the rest point, Lyapunov exponent and dimension are analyzed in detail using mathematical approach. Then the proposed system is inspected using bifurcation and Lyapunov exponent tools to verify the hyperchaotic behavior of the system. The numerical simulations indicate that the proposed hyperchaotic hyperjerk system has complex and wealthy dynamics.