CRISIS TRANSITIONS IN EXCITABLE CELL MODELS

It is believed that sudden changes both in the size of chaotic attract or and in the number of unstable periodic orbits on chaotic attractor are sufficient for interior crisis. In this paper, some interior crisi s phenomena were discovered in a class of physically realizable dissip ative dynamical systems. These systems represent the oscillatory activ ity of membrane potentials observed in excitable cells such as neurona l cells, pancreatic beta-cells, and cardiac cells. We examined the occ urrence of interior crises in these systems by two means: (i) construc ting bifurcation diagrams and (ii) calculating the number of unstable periodic orbits on chaotic attractor. Bifurcation diagrams were obtain ed by numerically integrating the simultaneous differential equations which simulate the activity of excitable membranes. These bifurcation diagrams have shown an apparent crisis activity. We also demonstrate i n terms of the associated Poincare maps that the number of unstable pe riodic orbits embedded in a chaotic attractor suddenly increases or de creases at the crisis.