Heterogeneous multistability in a novel system with purely nonlinear terms

In this paper, the dynamic properties of the new 3-Dimensional autonomous system without linear terms are investigated. The nonlinear features of the explored model are highlighted in terms of bifurcations, time traces, phase portraits as well as space magnetisation graphs. Several striking phenomena are found including, periodic and chaotic oscillations, periodic windows, coexisting (symmetric and asymmetric) attractors known as the heterogeneous multistability, coexisting bifurcation branches, symmetry-restoring crisis scenario, offset-boosting properties while varying the system parameters. Compared to some interesting cases previously recorded on systems with no linear terms, the repertory of behaviours found in this work represents a unique contribution in comparison with such type of systems. A suitable analog computer is constructed and implemented to support the numerical analysis via PSim-based analogue simulations.