| The spiral wave is a non-equilibrium form of patterns, it is widespread in nature,such as cardiac electrical activity spiral wave after arrhythmias, spiral-wave pattern inthe accumulation of sticky bacteria formation and spiral galaxies in the celestial body,it involves many disciplines such as physics, medicine, mechanics, biology,mathematics, chemistry and astronomy. The systems of spiral wave are typicallynon-linear, spiral-wave state is far from equilibrium, self-organization, so the spiralwave provides a number of problems for the theoretical study. Research of spiralwave has important implications in the theory and practical application, the relevantresearch has been carried out extensively, spiral wave dynamics behavior underexternal force is an important direction of the spiral wave research, this thesis studythe spiral wave dynamics by external force and dichotomous noise driving, the mainwork:Part I: Studying the affect of external force for dynamics of spiral wave (this part ofthe work is focused on Chapter2of the paper). Take external force from anotherspiral wave of excitable system (known as the drive system), the dynamic behavior ofdrive spiral wave are regularly changing with driving strength, driving wave centrallocation and the excitable parameter of driving and drive system. Stimulatedparameters of the driving and the drive system can be same, if the center of two shockwave are very near, the center of the driving wave would be attract to the center of thedrive wave, the center of the drive wave is directly attract to the center of the drivingwave, attraction can increase due to increasing of driving strength, the center locationof the two drive wave far away from will destroy this attractive interaction to form anew law. Overall, if the drive strength is little, the dynamics behavior of drive spiralwave can be understood the dynamic behavior without external drive and coupledwith the overall small changes of the motor unit, the impact of the drive wave is alsogrowing with the intensity increase, it has different manifestations in different shockparameters system. The article also discusses the condition of eliminate spiral waveby external force. Part II: Research the effect of dichotomous noise on the dynamics of spiral wave(this part of the work is focused on Chapter3of the paper).Spiral wave dynamicsshow regular changes under the action of dichotomous noise with noise intensity, timecorrelation parameters, this rule change can be explained by spectral analysis. Thedichotomous noise introduced will destroy the modulation track in original roamingorbital, this crushing effect will exacerbate with increased of noise intensity ortime-correlated parameters, showing modulation peak widening and amplitudedecreasing in the analysis of spectral, the modulation peaks will disappear when thenoise intensity or time correlation parameter is relatively large. On the other hand, ithas little effect for the essential rotary motion and essential rotary motion cycle ofspiral waves of the dichotomous noise. When the noise intensity or time correlationparameters are very great, dichotomous noise can be driven the head of spiral wavequickly moving to the no-flux boundary and disappear from there, providing a methodto eliminate spiral waves by dichotomous noise. |
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