Theory and design of a bio-inspired multistable oscillator

We propose a semi-autonomous low-dimensional dynamical system that possess numerous coexisting stable oscillatory solutions. Unlike previous multistable systems, our system does not explicitly depend on delayed feedback. This system is inspired by earlier work studying the multistable dynamics in biological models of electrical activity in bursting neurons. The model consists of a second-order underdamped linear system that receives pulsatile input over a subregion of the state space. Simulation results illustrate numerous stable coexisting periodic solutions that are both robust and easy to switch between. We demonstrated the feasibility of this system by building and testing an analog circuit implementation of this model system. The analog circuit possess four or more coexisting solutions. Read out of the current state of the system is trivial due to the nature of the circuits dynamics, and the state of the system may be switched by appropriately timed inputs.