Dynamics and circuit emulation of an extreme multistable system of two linear and one nonlinear coupled oscillators with hidden attractors

A system of two linear oscillators coupled to a damped nonlinear oscillator that has multiple stability and hidden chaotic attractors, is studied in this work. The unperturbed Hamiltonian part contains, apart from the quadratic harmonic oscillations, a nonlinear fourth order term with extra linear part with respect to the first two oscillators. As a consequence the proposed system has only one equilibrium point that is non-hyperbolic. Also, the chaotic attractors of the full system are hidden i.e. their basin of attraction does not have any unstable equilibrium point. Furthermore, the electronic realization of the system is presented and its dynamical behavior is studied in order to confirm the feasibility of the theoretical model. © 2019, North Atlantic University Union. All rights reserved.