Multiple steady states and dissipative structures in a circular and linear array of three cells: Numerical and experimental approaches

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Abstract
The steady‐state behavior of a circular and linear array of three cells containing a substrate‐inhibited‐like kinetics catalyzed by immobilized thylakoids is studied. The photobiochemical reaction used to model the system is based on previous studies concerning a single and a two‐cell system. In a general model all the cells in the array are considered to be continuously fed by the substrate and under diffusional relation with each others. Several models are then considered (circular and linear arrangements) depending upon the presence or the absence of these previous characteristics on each cell. The behavior of the various configurations is studied as a function of both the external substrate input concentration a 0, and the ratio between the transport terms λ. The results given by bifurcation analysis and limit point continuation allows to determine three domains of stable stationary behavior: I, monostability; II, bistability and multistability; III, multistability and occurrence of dissipative structures. The existence of domain III is strictly dependent on the existence of a topological and functional symmetry in the arrangement. The experimental occurrence of both stable symmetric and asymmetric steady states in a circular and linear array of cells is also illustrated.