Multistability is a critical property of nonlinear dynamical systems, where a variety of behaviors such as coexisting attractors can appear for the same parameters, but different initial conditions. The flexibility in the system’s performance can be archived without changing parameters. Complex dynamics have been observed in multistable systems, and we have witnessed systems with multistability in numerous fields ranging across physics, biology, chemistry, electronics, and mechanics, as well as reported applications in oscillators and secure communications. It is now well established from a variety of studies that multistable systems are very sensitive to both random noise and perturbations, and numerous studies such as open-loop control, feedback control, adaptive control, intelligent control, and stochastic control have been attempted to control such systems.

Recent attention has focused more on extraordinary cases of systems with multistability, such as systems with megastability and extreme multistability. A megastability system can display a countable infinity of coexisting attractors, whereas an extreme multistability system can exhibit an uncountable infinity of coexisting attractors. However, there are still various theoretical and technical issues which should be investigated in such systems. Circuit design (numerical and hardware) of multistable systems is also a related research problem with real-world applications, and fractional order modeling and realization of multistable systems constitute also a complex and challenging task. Furthermore, circuit realizations (simulations and hardware design) of multistable systems are useful for various practical applications in engineering.

This special issue aims to introduce and discuss novel results, control techniques, and circuit simulations for complex nonlinear systems with multistability. We welcome original research and review articles relating to the themes of this special issue.

Potential topics include but are not limited to the following:

• Advanced modeling approaches and analyses of nonlinear systems with multistability
• Circuit realizations of multistable systems
• Coexistence of attractors (self-excited and hidden ones)
• Complex dynamics and extraordinary features of nonlinear systems with multistability
• Complexity and estimation methods for applications in nonlinear systems with multistability
• Fractional order modeling and control of multistable systems
• Novel control and synchronization techniques for multistable systems
• Numerical techniques for multistable systems
• Practical multistable systems and potential applications
• Secure communications using multistable systems