Double Excitable Dynamical Behavior Of The System And The Spiral Wave Control

On the basis of the dynamics of spiral waves in single layer and the control methods which have been put forward, the dynamical behaviors of spiral waves in two identical layers and the control of spiral waves are studied, and the effect of noise on spiral waves which will be break up if the excitability is strengthen, is also considered . The following works are done:First of all, the dynamics of two identical layers are studied. When travel waves exist in the system, unidirection synchronization, bi-direction synchronizaion and travel wave source emerge in different values of couple strength. As to spiral waves, there appear synchronization of spiral wave, synchronization of multiple spiral waves, elimination of spiral waves that has three situations, and asynchronization of spiral waves for different couple strength separately. In the third chapter, we also study the motion of tips. With strengthening of the excitability, the meander appears in single FHN layer. When the synchronization and asynchronizaion of spiral waves happen, the tip orbits of spiral waves in first layer are offered.Secondly, the dynamical behaviors of two identical layers with time-delayed couple are studied. The existence of the stable state in single point depends on couple intension and delay time. When stable state is missing, there is reverse synchronization relation between the first layer and the second one. In the range of the parameter, multi-armed spiral waves and segmented spiral waves can be observed, and segmented spiral waves are different from the one in BZ-AOT microemulsions. If the parameters are selected to guarantee existence of the stable state, dynamical behaviors can be seen, which are similar to the ones in the third section.Further more, the relation of perturbation period and excited period on one point discussed. On the basis of this, the method of controlling spiral waves and spatiotemporal chaos is put forward. For the pulse trains without alternation, there are many segments of linear relation between excited period and perturbation period, which correspond to 1:1, 2:1, 3:1 relation and so on. It can be understood by the knowledge of the vulnerable period and absolute refractory periods. For the pulse trains of harmonic alternation, the relation of 3:2 can be observed. As a result of absolute refractory, the collision of two excited parts leads totheir disappearance. The result of pulse trains competing with spiral waves relies on their excited periods separately. On the basis of these studies, we give a method to control spiral waves and spatiotemporal chaos. In this method, periodic perturbation that is similar to periodic pacemaker in heart sinus cell is applied to the region near the left boundary, and perturbation period is selected according to the above relation between perturbation and excited period. The efficiency of control is tied up the difference of the excited period between pulse trains and spiral wave or spatiotemporal chaos. The method is general and can be against noise.Finally, the effect of spatiotemporal noise on spiral waves is studied, when the parameters are selected to approach the corresponding ones of the instability. Noise can lead to the breakup of the spiral waves. Deeper discussion is in progress.