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.

本文的目的是分析和控制生物捕捉振荡器的超混沌行为。我们主要在经典和分数演算的框架中分别研究超混沌模型的混沌控制和同步。首先，分析了所考虑模型及其超混沌吸引子的相图。然后设计了两个有效的最优和自适应控制器，以补偿不良的超混沌行为。此外，应用有效的自适应控制程序，我们通常会同步两个相同的生物快动振荡器模型。最后，针对所考虑的振荡器提出了一种新的分数模型，以获得超混沌吸引子。的确，分数演算可以产生具有记忆效应的更现实，更灵活的模型，这可以帮助我们设计更高效的控制器。考虑到此功能，我们分别应用线性状态反馈控制器和主动控制方案来控制超混沌并实现同步。通过获得的模拟和实验在数值上证明了相关的理论结果。