Chaos, Bistability and Extreme Event in an Oscillator with Offset Boosting and Amplitude Control

Chaos and extreme events are characteristic manifestations of the complex and often unpredictable behavior of nonlinear dynamical systems. In this study, we introduce an oscillator capable of exhibiting both chaotic dynamics and extreme events. The proposed oscillator incorporates quadratic and absolute-value nonlinearities, which contribute to its rich dynamical behavior. A key feature of the system is the simultaneous availability of offset boosting and amplitude control without requiring changes in the initial conditions. By varying only the control parameter b, the oscillator exhibits a variety of dynamical regimes, including chaos and extreme events. Furthermore, bistability is demonstrated by varying the initial conditions, leading to the coexistence of distinct attractors for identical parameter values. An analog electronic circuit is designed to realize the proposed oscillator, demonstrating its feasibility for practical hardware implementation. The proposed system therefore provides a simple and flexible platform for investigating complex attractor dynamics, including chaos, extreme events, and bistability, while offering convenient control over the amplitude and offset of the generated signals.