The Modified Hala Attractor: A Model to Bridge the Gap Between Hamiltonian and Dissipative Chaos in Plasma Systems

This paper introduces and computationally analyzes a modified version of the Hala attractor as a chaotic system designed to bridge the gap between dissipative and Hamiltonian dynamics. The model incorporates a tunable dissipation parameter, δ, and an external periodic forcing term to simulate resonance in physical plasma systems. Through numerical simulations and a detailed analysis of Lyapunov exponents and phase space trajectories, it was demonstrated that the system's chaoticity and dissipative properties can be independently controlled. It is shown that the system can transition from a non-chaotic, dissipative state to a chaotic, non-dissipative (Hamiltonian-like) state. This novel approach provides a framework for modeling phenomena in plasma physics, such as wave-particle interactions and collective behavior, where the degree of chaos is not an inherent property but a controllable variable. The findings validate the utility of tunable chaotic systems for advanced applications in engineered chaotic processes.