Dynamics And Control Of Spiral Waves Under Feedback From Moving Measuring Points

Spiral waves and spiral turbulence through spontaneous instabilities of spiral waves are harmful in some systems.In the myocardial tissue,for example,they are closely associated with cardiac diseases such as arrhythmia and ventricular fibrillation.Therefore,the model of control need to be developed to eliminate them.During the treatment of ventricular fibrillation,a strong electric shock is usually used to stop the electrical activity in the myocardium.This method can be painful and risky for the patient.It has an important practical significance about the development of effective low-energy control methods.Experimental results show that some shock-free scheme also effective for cardiac defibrillation,such as the use of optogenetic technology to treat arrhythmia.Some schemes have also been proposed in theory,such as method for local perturbations,method to create moving local heterogeneity,wave-driven approach in the weak space and the method of driving it with a rotating electric field.Here,we control the spiral wave in the Fitz Hugh-Nagumo(FHN)model with the feedback method which utilizes the mobile feedback point,and detailed study the dynamical behavior of the spiral waves under the effect of this feedback.The specific work is divided into three parts as follows.The first part: We study the controlled case of the spiral wave when the moving measurement point is fixed relative to the tip of the spiral wave.It is pointed out that this feedback can drive the drift unit of the spiral wave to drift along a linear path to the boundary and disappear from the no-flow boundary.There are some change rules of drift velocity,drift direction and drift cell shape with some parameters that include feedback strength,distance from the measurement point to the tip of the spiral wave,orientation of the measurement point relative to the spiral wave tip,position of the tip of the spiral wave in the spline track when feedback is activated and system excitability parameters.When the feedback strength is small,the drift unit will basically maintains the original flower pattern.As the intensity of the feedback increases,the flower pattern will gradually open,and the drift speed and drift direction angle will increase nonlinearly or linearly.There is a linear relationship between the drift direction angle and measurement point relative to the azimuth of the spiral wave tip.The distance between the measurement point and the spiral wave tip affects the intercept of the linear relationship and there is a periodic relationship.When feedback is activated,the spiral wave tip located on different petals will drift quickly in the same direction,although these spiral wave tips initial drift direction is different.Factors such as excitability parameters also have important influences on the dynamical behavior of controlled spiral waves.The second part: We study how the spiral wave is controlled when the moving measurement point changes relative to the orientation of the spiral wave tip.The situation is considered where the moving measurement point is constrained on the tangent of the helical contour at the spiral wave tip and a straight line with a certain angle to the tangent where the spiral wave tip passes.It is pointed out that feedback can control the radius of the modulation circle in the trajectories of the spiral tip and also enable the transition from the roaming spiral wave to the rigidly rotating spiral wave.The change rules of the transition between hypocycloid and epicycloidal of the trajectories of the spiral wave tip,the radius of the modulation circle with feedback strength,the distance from the feedback point to the spiral wave tip,the angle between the constraint line and the tangent line,the excitability parameter and the delay time are given.The feedback has little effect on the rigidly rotating spiral wave(with large system excitability parameters)and the active area of the spiral wave tip is small(with small system excitability parameters),but it can be well controlled for the spiral waves under the intermediate excitability parameter.On the two sides of the linear drift corresponding to the excitability parameter,the rolling situation of the spiral wave tip is different,usually in two cases: hypocycloid and epicycloidal.The control can stabilize the radius of the modulation circle,change the excitability parameter of the linear circular roll drift,and eliminate the phenomenon of the linear circular roll drift.They show regular changes with the control parameters and system parameters.The third part: The effect of feedback signals derived from multiple moving measurement points on spiral wave dynamics is investigated.The orientation of each measurement point is fixed relative to the spiral wave tip.We consider various forms of feedback,point out that multi-channel feedback also causes the centre of the spiral wave to drift along a straight line to the boundary,and give some laws about the direction of drift,the speed of drift and other factors as a function of the feedback parameters and the system parameters.