Conditional Lyapunov Exponents for Izhikevich Neuronal Model: Preliminary Results
Filipe Ieda Fazanaro1; Ricardo Suyama1; Diogo Coutinho Soriano1
1 UFABC
Resumo
The Izhikevich neuronal model has been adopted as an important benchmark in theoretical neuroscience, and exhibits one of the best relations between biological plausibility and computational cost. The present work aims to analyze the synchronization between unidirectional coupled Izhikevich neurons by means of the conditional Lyapunov exponent evaluation. In order to overcome the analytical difficulties imposed by its discontinuous structure, we apply a saltation matrix theory to the variational equations. The generalization of these results for bidirectional couplings in electrical and chemical contexts stand as natural perspective of this work.
Palavras-chave: Conditional Lyapunov Exponents; Discontinuous Dynamical Systems; Izhikevich model; Nonlinear Systems and Neural Dynamics; Synchronization in Nonlinear Systems