Temporal Self-organization of the Electrode B-Z System Controlled Externally by Weak-Periodical Current Constraint

The coupled dynamical model consisting of the electrode B-Z system, and its related bulk phase B-Z system externally controlled by a periodical current is proposed on the basis of the Oregonator model. Dynamical behaviors of the electrode B-Z system, when subjected to external current constraint have been investigated systematically under the condition that the bulk phase is at a steady state. Furthermore, by means of the analytic method of slow manifold the regimes favorable to the appearance of limit-cycle oscillation have been determined on both the current~concentration of BrO3- and the current~model parameter plane respectively. The results are similar to those of experiments controlled externally by weak-periodical potential constraint, as reported in former works. It turns out that a limited cycle oscillatory regime degenerates under external periodical current constraint. Meanwhile, a kind of forced oscillations emerges in the regime where limit-cycle oscillations can t appear under constant current constraint.