Dynamics of Evolution of Mira 2 System: Chaos and Complexity

The evolutionary states of the Mira 2 system in various parameter spaces (A, B) have been thoroughly investigated. The existence of fixed points within the system has been demonstrated, contingent on specific conditions between A and B. In light of these findings, bifurcation diagrams have been generated for two scenarios: first, with parameter A held constant while varying parameter B, and second, with parameter B held constant while varying parameter A. These bifurcation diagrams reveal a rich spectrum of complex dynamical behaviors. Intriguingly, both regular and chaotic attractors have been observed for different combinations of (A, B) values. Lyapunov exponents (LCEs) have been computed for both regular and chaotic evolutions, with LCE < 0 for regular cases and LCE > 0 for chaotic instances. As the system exhibits increasing complexity during its evolution, topological entropies have been calculated as a measure of this complexity. Furthermore, correlation dimensions have been determined to gauge the dimensionality of chaotic attractors.