Effect Of Local Inhomogeneity On Spiral Wave Dynamics In Excitable Media

Spiral waves as a form of a non-equilibrium patterns commonly found in excitable media, oscillation media and the bistable system, and it is a typical object of study related to spatial and temporal structure and evolution in the nonlinear science, its theory and application are both important. It can involve multiple areas of discipline such as physics, biology, mechanics, astronomy, mathematics and chemistry. In this thesis, we use the FitzHugh-Nagumo model to simulate the dynamic behavior of spiral wave in the inhomogeneous excitable medium, the main work is as follows:Firstly, we study effection of two partition inhomogeneous excitable medium on the formation of spiral wave patterns (this work is written in the second chapter). We keep the excitable parameter of the original wave tip region unchanged and change the excitable parameter of the region not including the tip. The spiral wave is almost unaffected when the two partitions dividing line is away from the original wave tip. when the dividing line close to the original wave tip, due to the heterogeneity of the entire space, the tip will be pulled to the region of the large parameters. Shock and parameter values, the local wavelength is relatively large, that is, the smaller the corresponding wave velocity. The value range of the dividing line effecting the tip depends on the excitable parameters difference between the two parts.Secondly, we research the spiral dynamical behaviors in local inhomogeneous excitable media (this work is written in the third chapter). When the circle does not contain the entire original tip, we keep the parameter of outside circle unchanged, changing its internal parameters and we found that when the internal excitable parameter is greater than the external one (ε1>ε2) the tip effected by excitability is attracted to the inner of the circle. And at this time if the tip can be attracted into the circle there must be a relation between size and location of the circle. when the circle contains the entire original tip, we also keep the parameter of outside circle unchanged, changing its internal one and we observed that when ε1>ε2the tip is attracted into the circle. When ε1<ε2the original tip would be excluded outside the circle and move around the limit cycle attractor being the concentric circle of the original tip center. At the same time we also investigated the situation that the internal parameter is not changed, changing the external one and found that the final results are the same as above. In addition, we also found that when the circle contains the entire tip meeting the condition of the internal and external parameters difference bigger there is a phenomenon that the spiral is snapped, and in different condition the broken situation is different:when the radius is smaller the spiral will broke only once. When the radius is bigger the spiral would emerge intermittent breaking. Additions, when the circle not containing the entire tip is changed into a removable circle and meets certain condition the tip effected by its excitability would appear the phenomenon that it moves along the circle and is pulled out the boundary.Finally, we study the spiral dynamical behaviors in the excitable media of several local inhomogeneity. It is founded that different forms of local non-uniform region, have different effects on the dynamic behavior of spiral waves. When the several circles lined in a row, the appropriate value can make the tip do movement effected by the several circles, which provided the conditions for controlling the spiral wave. When the area is double-row several circles, the phenomenon and situation will appear that the tip will move between the double-row or move some time and then along the internal edge of the entire space.