| Pattern dynamics is one of the important branches of the nonlinear scientific field.The study of pattern dynamics can occurs in various fields including physics,mechanics, mathematics,biology,ecology, and so on.Pattern has an inhomogeneous spatiotemporal macrostructure.it is universal existence in nature.Patterns in nature can be classified into two types:The first type of pattern is the pattern of thermodynamic equilibrium,such as the crystal structure of inorganic chemistry,self-organized pattern in organic polymers.The second is the pattern of thermodynamic non-equilibrium.The spiral wave is one of the most common non-equilibrium patterns.It can be observed in some physical,chemical and biological systems,such as the Ising-Bloch phase change,the self-organization of gummy fungi,the BZ reactions,the electrical signal in cardiac,and the waves of calcium ion in oocyte.It is well known that spiral wave is harmful to the heart system.The reason is that the emergence of spiral wave in the myocardium can lead to tachycardia and even leads to cardiac arrhythmia or ventricular fibrillation if the spiral wave is broken up into spatiotemporal chaos.Therefore,how to eliminate spiral waves in cardiac tissues as well as develop method of defibrillation depend on the widespread research of the nonlinear scientist.That is why so many researchers study spiral wave in the recent years.The excitable medium is a reaction-diffusion system,and is one of most simple systems in which spiral waves can be generated.In this paper,we apply B?r model to study the effect of the defect defined by failure of the diffusion effect on dynamics of spiral waves in two-dimensional excitable media.The formation of self-sustained target waves and evolution of symmetrical patterns in the excitable media with a ring-like heterogeneous excitable medium are investigated.ChapterΙis the summary.The basic characteristic of chaos,typical reaction-diffusion systems,the nature of the excitable medium,some excitable system model,and the formation of spiral waves are briefly introduced. Chapter II introduce the influence of the defects without diffusion function on dynamics of spiral wave.The B?r model is considered.The influence of the defect,defined by failure of the diffusion effect,on dynamics of spiral wave is investigated by introducing the system some defects.These defects are uniformly distributed.It is numerically found that these defects can lead to the reduction of the excitability of medium and wave speed. When the number of defect is large enough,these defects can induce the meandering or the breakup of an originally stable spiral wave.On the other hands,the defects can yet cause an unstable spiral wave to become a rigidly rotating or meandering spiral wave.The phenomenon that Doppler Effect cause unstable spiral wave to break up into co-existence state of spatiotemporal chaos and small spiral waves is observed for the first time.The physical mechanism about these phenomena are briefly discussed.The formation of self-sustained target wave in two-dimensional excitable medium with a ring-like heterogeneous excitable medium is investigated in chapter III.The numerical results show that the initial perturbation can produce a self-sustained target wave in an excitable medium when the excitability of two media and the size of the ring are properly choice.The physical mechanism underlying the formation of self-sustained target wave is analyzed. The study of Chapter IV is the continuation of the study of third chapter.We further study that the evolution of the symmetrical pattern generated by an initial external perturbation when the size of the ring-like heterogeneous excitable medium is large. We discovery a new phenomenon of spatiotemporal chaos,i.e.,the irregular excitation causes system being unable to reach its steady-state after the initial external disturbance.Thus,many new symmetric patterns are continuously generated.The physical mechanism of these phenomena is discussed. |
