Dynamics Of Spiral Waves Driven By External Force

In the present paper, Based FitzHugh-Nagumo model we study the spiral waves dynamics which driven by noise and periodic force, Lévy noise and feedback signal. Main work was done as below:1. The dynamics of spiral wave behavior which driven by noise and periodic force: We study the tip of spiral wave move with the frequency (period) which driven by periodic forces. And we find some phenomena such as:1:1 and2:1 resonance, straight line with petal element and intermittent straight line . Give the range of movement tip of spiral wave. And Given the average period of external frequency (or cycle) of the quantitative relationship in which far from the tip of spiral waves. Spectrum analysis can be used to explain the radius that 1:1 and2:1 resonance with both the increase with the force period.We find the spiral wave break occurs in a range between 1:1 resonance and 2:1 resonance. It is different from the Doppler and Eckaus instability .It is inspired by the partial wave caused by a two-way communication (long wavelength leading to the emergence of local two-way communication area).We study effects of noise intensity and amplitude of periodic force on he average period and standard deviation. And we find the effects of average period that far from spiral tip was greater than other scope. We study the relationship between modulation cycle and external cycle, the Arnold tongue is formed different intensity of noise and the period of periodic. We find noise play constructive role—resonance broadens (stochastic resonance).2 We study the dynamics of spiral wave behavior which driven by Lévy noise.In contrast to Gaussian noise, and Lévy density distrubations has heavy tail. The probability that Small-scale events appear is much higher , and it is also the emergence of large-scale events with skip. In order to prevent the emergence of excessive scale, we use the truncated Lévy noise. In the case of small intensity, Lévy noise impact on the range that spiral tip appear is smaller than the effect of the Gaussian white noise, indicating that the system is mainly affected by the impact of small-scale random variable. With intensity increased, the breaking of spiral occurs, the minimum intensity that spiral wave break indicate that Lévy noise is less than Gaussian white noise , because large-scale random variables play a part. We also find that mechanism which Lévy noise and Gaussian white noise caused the broken is different. The average cycle and variance are that away from the tip show them interpretation.3. We study spiral wave dynamics which two point feedback control. We find many different types of orbits when we fix a measuring point and change the location of the other measurement points. A limit cycles that move around the two points formed by the two measuring points very close (less than the wavelength of spiral wave).The tip track is changed by the changing larger distance between the two measurement point.The different tracks are displayed because of two measurement point compete with each other. We also discussed the effect of the dynamic behavior on which delay time, feedback signals come from different measuring points and gives some quantitative relationship.