A computational framework combining neuronal dynamics and evolutionary game theory for network-level synaptic interactions

<i>Objective.</i>In this study, we present a novel computational framework that combines the Hindmarsh-Rose (HR) neuronal model with evolutionary game theory on networks to simulate and interpret synaptic-level interactions within neuronal populations. Our approach preserves the features of the HR model-capable of generating both spiking and bursting dynamics-while integrating game-theoretic principles that govern the balance between emulative and non-emulative behaviors across neurons.<i>Approach.</i>Neurons were modeled as strategic agents whose interactions evolve according to game-theoretic principles, allowing us to capture emergent network dynamics beyond classical electrophysiological analyses. A key innovation of our work is the formulation of a parameter estimation method based on adaptive observers, which enables the recovery of game-theoretic parameters solely from partial state observations. The proposed framework is validated through numerical simulations, demonstrating its ability to recover hidden parameters and accurately predict system behavior under diverse conditions.<i>Main results.</i>By applying the devised approach to synthetic datasets mimicking real electrophysiological recordings, we highlight its applicability in distinguishing neuronal populations based on their strategic interactions. In this context, the model is shown to faithfully reproduce both spiking and bursting behaviors, capturing the diverse electrophysiological patterns observed in<i>in vitro</i>experimental settings. Furthermore, we explore the potential of this model in experimental data analysis by suggesting that the estimated parameters may serve as discriminative markers for different neuronal types and structural characteristics.<i>Significance.</i>The integration of dynamical systems theory, game-theoretic modeling, and adaptive estimation provides a robust quantitative tool for investigating complex neuronal network dynamics. Our results quantitatively demonstrate the scalability and accuracy of the method in parameter estimation, reinforcing its value for systematic analysis of synaptic interactions and advancing our understanding of neuronal network dynamics.