Energy computation and multistability in a class of second-order chaotic systems with simple nonlinearities: numerical, experimental and analytical results

The present work is aimed at the design, implementation and analysis of generic new second-order non-autonomous chaotic systems with simple nonlinear functions that have algebraically simple representations in mathematical form. These systems involve simple second-order non-autonomous ordinary differential equations with different simple nonlinearities like G(x)(=x2,∣x∣,max(x)andmin(x)) . The present study deals with numerical simulation, experimental analog circuit simulation results to demonstrate the ordered and chaotic phenomena being exhibited by these systems. Of most interest the striking phenomenon of multistability is uncovered for certain nonlinearities. Coexisting attractors are harnessed through the offset boosting approach. Also, the Hamilton energy is established through the Helmholtz theorem. It is found that both methods can be exploited as a non-bifurcation approach in characterizing multistability in the model. Further, analytical solutions developed for systems with certain nonlinearities are presented and the chaotic behavior of the systems studied using the solutions validating the numerical and experimental results are reported.