Superstructure Spiral Waves In Reaction Diffusion Systems

Spatiotemporal pattern formation in reaction-diffusion(RD)systems has been suggested to be an underlying mechanism that gives rise to complex patterns in biology.Kinetics of spot diagram is a horizontal science that researches the mechanism and laws of spot diagram from the Angle of dynamics.Spiral wave of reaction diffusion system is a typical example of self-organizing behavior.In this paper,by means of numerical simulation and theoretical analysis,we found some new types of complicated spiral waves and new ways which lead to destabilization.Specifically,in this paper,the main structure is as follows:In chapter 1,first briefly introduces the background of pattern dynamics,research field and research history,then introduces the pattern dynamics research methods and research significance.In chapter 2,this paper introduces the generation of spiral waves,roaming and instability,and the research status of experiment and numerical simulation of the spiral.The following is my main work in the graduate student stage.In chapter 3,we found in a new complex spiral waves,called oscillation wave arm spiral waves in Decroly-Goldbeter mode through the numerical simulationl.The whole spiral retains a perfect Archimedean structure until breakup which occurs in manner of the transverse split of spiral arm.The novel phenomena of arm oscillations and transverse split of spiral arm are attributed to superposition of spiral and another solution of the equations of the reaction-diffusion Decroly-Goldbeter mode,which is now believed to also be responsible for the formation and breakup of the previously observed spiral waves with superimposed target waves and theoretically have the potential to generate more kinds of complex spiral structures.And then simplified the mode.The novel phenomena of arm oscillations and transverse split of spiral arm are attributed to that the mode of transmission of the wave in this reaction-diffusion modeltakes the form of leap-frogging caused by that the flow in phase space is very sensitive to the excitation condition,which is now believed to also be responsible for the formation and breakup of the previously observed spiral waves with superimposed target waves and theoretically have the potential to generate more kinds of complex spiral structures.We get the conclusion that ‘arm-oscillatory' is the critical phenomena of excitability in this excitable medium.In chapter 4,we established a new model,and found in a novel bistable spiral waves,called stepwise spiral waves through the numerical simulation in the model.Prior to the period-doubling bifurcation of this system,the stepped spiral waves are produced by an unwanted phase trajectory event;the loss of symmetry takes the form of synchronization defect lines,where the trajectory in the local oscillation phase space changes into two different ways.The formation principle of this type of bi-stable spiral wave and the internal structure and geometry of these synchronization defects are studied,and several potential categories of stepped spiral waves are discussed.In chapter 5,to modify the model in the previous chapter,we made it into a steady state model.Some new kinds of bi-stable and multi-stable spiral waves,all named stepped spiral wave,are investigated in this paper.According to the initial conditions,the stepped structures show different properties.The stepped structures can survive forever as the boundaries(of the different oscillation states)go through the center of spiral.In some conditions,the stepped structures can form spirals,over-spirals,which have a rotation direction being the same to the original spiral wave.With the same method,we get more kinds of multi-stable spiral waves in another model which has the same property with the first one.In the sixth chapter,we introduced a new type of instability of spiral waves.Used a simplified model in the third chapter,in a small area near the wave tip places a periodic perturbation,the perturbation system may be amplified,lead to the instability of spiral wave away from the tip.By changing the parameters of the system,spiral waves will contrive to suppress the disturbance on the top of the wave.Finally come to a conclusion that wave arm oscillation is a reflection of spiral wave instability.Chapter 7 is the summary and prospect for the work of this paper.