| The spiral pattern is one of the most important research objects in the nonlinear field,and it is common in nature.There are spiral waves in convective motion of fluid,barrier discharge of dielectric,catalytic oxidation of CO on single crystal surface,phase transition in liquid crystal,formation of map tongue,electrical activity signal in heart-brain system.In the heart-brain system,the theoretical and numerical study of spiral wave dynamics has important theoretical significance for the treatment of tachycardia,the prevention of ventricular fibrillation and the occurrence of some brain diseases.In this paper,the effect of moving heterogeneity and non-local feedback on the spiral wave dynamics is studied by the FHN model of the system and the CGLE of the oscillation system.The main work is as follows:Part ?:The dynamical behavior of spiral wave in the presence of moving heterogeneity is studied by using the FHN model of the excitable system.At the initial time,the excitability in the small sector with a width of A(p is changed and the heterogeneous region is formed.The heterogeneous region rotates with time at angular velocity ? around the center of the initial spiral wave.It is shown that when the change of excitability in the heterogeneity is weakened,the rotating movement of the heterogeneity can lead the spiral wave tip to the boundary and disappear at the no-flow boundary,which leads to the elimination of the whole spiral wave.When the spiral wave is eliminated,the weaker the excitability in the heterogeneity,the larger the optional range of the angular width of the heterogeneous region.Within the parameter space of the angle width of the heterogeneity and the heterogeneous excitability parameter,a small slit in the spiral wave-eliminating parameter region is proved to be related to the shape of the selected excitable medium.In the case of spiral wave survival,the relationship between the frequencies in the spiral tip motion and the rotation frequency in the heterogeneous region is also discussed,and it is found that there is a rational locking behavior between the two.The existence of fixed-frequency relation in the range of the rotating frequency range can be used to understand the change of the spiral tip movement when the movement of the spiral tip changes with the rotation frequency.Part ?:The influence of circular feedback on the spiral wave dynamics in the oscillation system is studied with CGLE.The feedback signal of circular feedback is calculated according to the wave activity in a circular region of the system.The spiral tip is located at a fixed point before the feedback signal is added to the system.The results show that when the feedback control is turned on,the spiral tip will have a transient drift,and then it will enter into the circular attractor or point attractor,and the point attractor will be located in the center of the circular measurement area.The circular attractor is concentric with the measuring area and has some discrete radius values.The selection of the final attractor by the spiral tip depends on the distance between the measurement center and the initial position of the spiral tip and the direction of the drift of the spiral tip when the spiral tip is first started,and the mode of the feedback signal after entering the circular attractor is constant.In the complex plane,the trajectory of the feedback signal changes with time is a circle,and the motion of the wave head can be obtained by analytical analysis.We also analyze the variation of the spiral tip motion with the measurement region scale,feedback gain,delay time and system scale parametersPart ?:The influence of ring feedback on the dynamics of spiral wave in oscillatory system is studied by CGLE.The study shows that with the change of the thickness or radius of the ring measuring area,the spiral tip can alternate between the point attractor and the circle attractor.We also give some variation of the spiral tip movement along with other parameters. |
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