Analysis And Application For The Stability Boundary Bifurcation Of Impulsive Switched Systems

The study of impulsive switching system is an important part of nonlinear dynamics.It reveals the nonlinear characteristics of the impulsive switching system from the perspective of dynamics,which has attracted the attention of many scientific workers in many scientific fields at home and abroad.As one of the research hotspots in the current field of nonlinear dynamics,especially in the passive dynamic walking field,the impulsive switching system has been fully used.But the system is different from the general continuous system which many general theory cannot be directly applied to the actual system.The complexity analysis method needs to simplify the system with the help of Poincaré map,and then use the typical Lyapunov Exponents algorithm to calculate the trajectory change scale,so as to obtain the complex behavior of the system.And then we calculated the natural periodic gait of the system,and simulated the results by numerical calculations tools.This article explained the following points:First of all,this paper analyzed and summarized the existing impulsive switching algorithm based on the existing theory of nonlinear dynamics,and proposed a new Lyapunov Exponents algorithm combined with numerical simulation.This algorithm can achieve the dynamic behavior of nonlinear at the full range observation system to effectively calculate the N dimensional impulsive switched systems in N direction change of LE scale.Finally,using this algorithm to calculate the typical pulse switching system is passive walking model,compared with the traditional Poincaré map method,verified the validity of the improved algorithm.Secondly,in view of the existing impulse stability parameters of switched systems are mostly based on the random search algorithm to find the effective range of the participation mechanism,but this method of parameters is not clearly identified,which is more based on the user experience to define the scope of the search and have low efficiency waste of computing resources,so it is difficult to apply the existing research results to more complex and practical models.Based on the Newton iteration method,the parameter search algorithm is improved in this paper.At the same time,the extension of the method is applied to the Compass-like data model,the correctness of the single valued extension algorithm is proved,and the limit inclusion relation between the passive model is proved.Thirdly,this paper introduced the T-Joint model of the pulse switching system,and proposed the system model and calculated the effective range of the system parameters by the single value extension algorithm.By using continuation algorithm to calculate the T-Joint model to be able to walk in step under small variation of the maximum and minimum slope angle calculation system application domain of attraction cell mapping method,the system initial value of suction,the results showed that this model has stronger anti-disturbance performance.