A New Conservative Chaotic Jerk System with Initial Offset Boosting for Energy Optimization

It is well known that the conservative chaotic system does not have phase portraits and also does not support reconstruction of phase portraits. Due to this complex behavior, the chaotic systems have many applications such as energy optimization. In this work, a new conservative chaotic jerk system is reported for energy optimization applications which have an infinite number of rest points. The new system has only one nonlinear term which is based on a sine function. The conservative chaotic systems present chaotic behavior along with the energy conservativeness. The detailed analysis of the dynamics of the proposed system is conducted using Lyapunov exponents and bifurcations. It is also shown that the proposed system has infinite number of saddle-foci equilibrium points and unstable. Finally, the initial offset boosting characteristic is realized in the proposed system for the variation of the initial conditions. By leveraging the principles of conservative chaotic systems, sustainable energy systems can become more efficient, resilient, and adaptable, ultimately supporting the transition to renewable energy sources.