Chaotic patterns in a coupled oscillator-excitator biochemical cell system

In this paper we examine dynamical modes resulting from diffusion-like inte raction of two model biochemical cells. Kinetics in each of the cells is gi ven by the ICC model of calcium ions in the cytosol. Constraints for one of the cells are set so that it is excitable. One of the constraints in the o ther cell-a fraction of activated cell surface receptors-is varied so that the dynamics in the cell is either excitable or oscillatory or a stable foc us. The cells are interacting via mass transfer and dynamics of the coupled system are studied as two parameters are varied-the fraction of activated receptors and the coupling strength. We find that (i) the excitator-excitat or interaction does not lead to oscillatory patterns, (ii) the oscillator-e xcitator interaction leads to alternating phase-locked periodic and quasipe riodic regimes, well known from oscillator-oscillator interactions; torus b reaking bifurcation generates chaos when the coupling strength is in an int ermediate range, (iii) the focus-excitator interaction generates compound o scillations arranged as period adding sequences alternating with chaotic wi ndows; the transition to chaos is accompanied by period doublings and foldi ng of branches of periodic orbits and is associated with a Shilnikov homocl inic orbit. The nature of spontaneous self-organized oscillations in the fo cus-excitator range is discussed. (C) 1999 American Institute of Physics. [ S1054-1500(99)02201-6].