Global and multistable dynamics in calcium oscillations model

Abstract

In most animal and plant cells, the information’s processing is insured by calcium ions. This contribution studies the global dynamics of a model of calcium oscillation. From the stability analysis, it is found that the oscillations of that model are self-excited since they are generated from unstable equilibria. Using two-parameter charts, the general behavior of the model is explored. From the hysteresis analysis using bifurcation diagrams with their related Largest Lyapunov Exponent (LLE) graphs, the coexisting oscillation modes are recorded. This phenomenon is characterized by the simultaneous existence of periodic and chaotic oscillations in the considered model by just varying the initial conditions. Using a set of parameters for which the model exhibits multistability, the basins of attraction related to each coexisting solution are computed and enable the capture of any coexisting pattern.