Chaos control and stabilization of a hybrid chaotic oscillator through deterministic and stochastic resets

We study the control of chaotic dynamics in the hybrid Nakano-Saito oscillator through periodic resetting schemes. In contrast to most existing approaches, which rely on Lyapunov-based constructions or optimization-driven control strategies, we focus on the underlying dynamical mechanisms responsible for the emergence of controlled and uncontrolled regimes. By analyzing the associated impact (return) map, we identify well-defined control windows that give rise to stable periodic solutions and investigate their dependence on the ratio γ between the oscillator’s natural frequency and the control frequency. We provide an analytical proof for the existence of a limit cycle and use this result to characterize the main control windows of the system, revealing distinct bifurcation phenomena that enable different regimes of chaos control within this canonical hybrid framework. Finally, we examine a stochastic resetting protocol governed by an inverse Gaussian distribution and show that it can outperform deterministic control schemes subject to timing jitter, achieving enhanced stabilization. These results demonstrate that classical dynamical systems tools are sufficient to derive precise control conditions and to assess control effectiveness even in stochastic hybrid settings.