A New 4-D Hyperchaotic System with No Rest Points for Energy Harvesting Applications

Energy harvesting using chaotic systems involves capturing energy from various ambient sources by leveraging the inherent dynamics of chaos. This approach can significantly enhance energy capture efficiency and adaptability in diverse applications. Chaotic systems exhibit sensitive dependence on initial conditions and unpredictable behavior. This can be exploited to optimize energy harvesting by enabling systems to respond dynamically to environmental fluctuations. The main contribution of this research work is the reporting of a new hyperchaotic system which has no rest points. The new system has only two quadratic nonlinear terms and three system parameters. The basic properties of the new system such as Lyapunov exponent, Lyapunov dimension, rest points are analyzed in detail. It is interesting that the new system is symmetric about the r-axis. The detailed analysis of the dynamics of the proposed system is conducted using Lyapunov exponents and bifurcations. It is also shown that the system has chaotic and hyperchaotic behavior for the particular range of parameter. Finally, the offset boosting characteristic is realized in the proposed system for the variation of the control parameter.