Adaptive Multi-Switching Chaos Synchronization of Lotka-Volterra Model to Replicate Complete and Anti-Behavior of Hindmarsh-Rose Neuron Model

Résumé

The generalized Lotka--Volterra ($\mathscr{L}$–$\mathscr{V}$) model, widely known for describing predator–prey population interactions, and the Hindmarsh–Rose ($\mathscr{H}$–$\mathscr{R}$) neuron model, a cornerstone in computational neuroscience, represent two distinct examples of nonlinear dynamical behavior in ecology and biology, respectively. In this work, an adaptive control framework is developed to achieve analytical results on multi-switching based hybrid projective synchronization between the $\mathscr{L}$–$\mathscr{V}$ and $\mathscr{H}$–$\mathscr{R}$ systems under eleven uncertain parameters. This approach relies minimally on exact parameter information, which enhances robustness and maintains efficient synchronization. Stability of synchronization errors is ensured through Lyapunov analysis. MATLAB simulations further verify the theoretical findings, demonstrating that synchronization remains successful despite the presence of multiple parameter uncertainties. Moreover, the framework encompasses several classical schemes, including complete synchronization, anti-synchronization, projective synchronization, and hybrid projective synchronization, as special cases. Alongside the synchronization results, a detailed dynamical analysis of the $\mathscr{L}$–$\mathscr{V}$ system is also conducted, providing additional insights into its complex nonlinear behavior.