DYNAMIC ANALYSIS AND HAMILTONIAN ENERGY ASPECTS OF HYPERCHAOTIC MEGASTABLE OSCILLATOR

Megastable oscillations are a subject of significant research interest due to their broad range of potential applications. Typically, megastable systems are driven into oscillation by a forcing term. In this paper, we propose a novel megastable oscillator that utilizes a combination of Signum and trigonometric functions. To the best of our knowledge, no 3D megastable system has been found to exhibit hyperchaotic behavior without any forcing term. We demonstrate the megastability of our oscillator using phase portraits and basins of attraction and confirm the oscillations using the Hamiltonian energy method. We also conduct a stability analysis to explore the system’s nature and investigate the impact of parameters using a bifurcation diagram. Furthermore, we present a Lyapunov spectrum to identify regions of chaos, hyperchaos, and periodic oscillations. The results we obtain demonstrate the complexity of the system and its sensitivity to initial conditions, making it well-suited for applications such as random number generation and secure communication.