Study On Control Of Spiral Wave Dynamics Properties By The External Field

Spiral wave is one kind of spatiotemporal pattern which is away fromthermodynamic equilibrium state, and widely exists in the nature. Research showsthat both of spiral and its break are harmful in many real systems. Such as the spiralwaves in cardiac can be a cause of tachycardia and repetitious breakup of waves canlead to ventricular fibrillation. Therefore, it is significant for many practicalproblems including the treatment of heartbeat tachycardia to find several effectivemethods to prevent and control spiral wave.Along with the development of computer science, nonlinear dynamics and themathematical model of cardiac action potential, the computer simulation and theanalysis of nonlinear stability have been an important and irreplaceable researchmethod which is used to explore and reveal the mechanism and control strategy ofventricular fibrillation. In this thesis, we use this method to study the dynamicproperties of the nonlinear wave and the associated control strategy.The chapters andstructure are arranged as follows:In chapter1, we briefly introduce the universal existence of spiral wave, thereaction-diffusion system, the formation of spiral wave and several partial differentialequation models which are used commonly in numerical simulation.From chapter2to chapter5, we elaborate four main results in detail which areachieved by the numerical simulation and analytical calculation.In chapter2, according to the perspective of time and space rotation symmetry,we add a rotating electric field in the excitable system to control the rotating spiralwave. We study the control of spiral wave under the driving of a rotating electric fieldand the influence of a rotating electric field on spiral dynamic properties. In ourstudies, we find a series of significant control effect: the rotating electric field candrive a spiral wave to be synchronous; a circularly rotating electric field can suppressmeandering spiral which is caused by Hopf bifurcation to rigid one; the rotatingelectric field can prevent breakup of spiral in medium with low excitability.In chapter3,we study the influences of periodic mechanical deformation（PMD）on pinned spiral waves. Firstly, we study the influences of the property of obstacle onpinned spiral wave, and find the phenomenon of embedding into or on an obstacle.Next, we give the dependence of meandering tip radius on the frequency of PMD.Then, we reveal the condition which is required when PMD can successfully remove pinned spiral waves. Finally, we make an exposition of three different unpinningmechanisms. Our results can make a contribution to understand the interactionbetween the action potential of the pinned spirals and the deformation in cardiactissue.In chapter4, for the first time, we propose a new method to remove pinned spiralwaves which is using a rotating electric pulse (REP) to excite an emitted wave on theobstacle (REF-WEH). By comparison with the traditional EP (electric pulses), we findthat REP can more effectively remove pinned spiral waves, and we also expound theadvantages and mechanism of REP in detail.In chapter5, we use Barkley model to study that using target waves which aregenerated by an external period force to remove one or more spiral wave which arepinned on the obstacle. We found that target waves not only can successfully removea spiral which is pinned on the obstacle, but also can successfully remove two or morespirals which are pinned on the obstacle.In chapter6, we make a brief summary about this thesis and put forward the futureprospect.In this thesis, we propose a series of synchronous control strategies and showsome significant results, some of which have certain innovation. We hope thesetheoretical and simulation results can be verified in related experiment.