Super extreme event and coexisting attractors in a novel chaotic snap system with hyperbolic sine function: Theoretical investigations and circuit experiments

Extreme events and multistability are among the most followed ongoing topics in nonlinear science due to their multiple potential applications in engineering. In this contribution, we introduce a new fourth-order autonomous hyperjerk (i.e. snap) system with a hyperbolic sine function. A detailed analysis of the proposed system is carried out thanks to analytical and numerical tools with special attention devoted to specific aspects such as the symmetry property, the analysis of the rest point, the derivation of the space volume contraction rate, and the routes to chaos when a parameter is gradually varied/monitored. By resorting to graphic tools such as graph of largest Lyapunov exponents, bifurcation diagrams, basins of attraction and phase space trajectory plots, we demonstrate that the new autonomous snap system owns striking nonlinear properties such as period doubling scenario to chaos, multistability, merging crises, offset boosting and extreme events as well. Experimental phase portraits acquired from an appropriately designed analog electronic simulator of the new snap model show good agreement with the theoretically predicted features. To the best of our knowledge, the presence of multiple coexisting stable states combined with the phenomenon of extreme events discussed in the present contribution is unprecedented in the literature, at least for a model as simple as the one discussed in the present work.