Design of multistability of chaotic systems via self and cross coupling

In this paper, we proposed general coupling conditions to the error dynamics of coupled dynamical systems for realizing multistability. The basic mechanism to propose multistability is to design partial synchronization of states between the coupled system and use to find some initial condition-dependent constants of motion. Here, we propose that i number of state variables are completely synchronized, and the remaining j number of state variables of two coupled systems are in constant difference to obtain multistable behaviour, where $$1\le i,j \le m-1$$ and $$i+j=m$$ . We interpret our scheme for coupled chaotic Lorenz, Rossler, and Van der Pol–Duffing oscillators. Further, we establish numerical simulation results with a bifurcation diagram, phase diagram, and maximum Lyapunov exponent to show the desired results of our schemes.