A new adaptive synchronization and hyperchaos control of a biological snap oscillator

Abstract

• Chaos control and synchronization of a biological snap oscillator is investigated. • Optimal and adaptive controllers are designed to overcome hyperchaotic behaviors. • An adaptive control scheme is introduced to synchronize two identical snap oscillators. • A new fractional model is developed for the biological system under study. • Efficient control strategies are used in fractional sense for the purpose of control and synchronization. The purpose of this paper is to analyze and control the hyperchaotic behaviours of a biological snap oscillator. We mainly study the chaos control and synchronization of a hyperchaotic model in both the frameworks of classical and fractional calculus, respectively. First, the phase portraits of the considered model and its hyperchaotic attractors are analyzed. Then two efficacious optimal and adaptive controllers are designed to compensate the undesirable hyperchaotic behaviours. Moreover, applying an efficient adaptive control procedure, we generally synchronize two identical biological snap oscillator models. Finally, a new fractional model is proposed for the considered oscillator in order to acquire the hyperchaotic attractors. Indeed, the fractional calculus leads to more realistic and flexible models with memory effects, which could help us to design more efficient controllers. Considering this feature, we apply a linear state-feedback controller as well as an active control scheme to control hyperchaos and achieve synchronization, respectively. The related theoretical consequences are numerically justified via the obtained simulations and experiments.