Bursting Oscillations And Mechanism Analysis Of Non-smooth Oscillators Under Slow-varying Excitation

Because of the wide background in engineering,the complicated dynamics of the non-smooth system with the coupling of multiple time scales has been becoming one of the hot and frontier topics in the field of nonlinear dynamics.In the thesis,we focus on two typical types of non-smooth nonlinear oscillators to investigate the complex dynamical behaviors of the systems with slowly-varying excitation.Different forms of bursting oscillations as well as the mechanism in the systems with two scales in frequency domain have been presented.The main work of this thesis is arranged as follows:1.The dynamical evolution with the variation of different parameters of a smooth Duffing system with single scale is analyzed,in which the cascading of period-doubling bifurcations between the periodic oscillations and chaotic movements is presented.Furthermore,different types of non-smooth attractors are obtained by exploring the behaviors of non-smooth Duffing system with the increase of the exciting amplitude.2.The dynamics of the slow-varying excited Duffing oscillator with cubic and fifth order nonlinear terms is investigated respectively.Several forms of bursting attractors with different equilibrium points and the bifurcations are presented.By introducing the transformed phase portrait,combining the equilibrium branches and their bifurcations of the fast subsystem with the variation of the slow-varying parameter,the mechanism of bursting oscillations is presented.3.The complicated behaviors of non-smooth Duffing system is explored,in which different bursting attractors with symmetric and asymmetric structures are observed,respectively.Since the non-smooth boundaries may influence the characteristics of the equilibrium points,different location of the boundaries may lead to different bursting oscillations.Meanwhile,in the non-smooth systems,both the conventional and non-conventional bifurcations may result in the transitions between the quiescent states and spiking states.4.For the parameters with different distribution of equilibrium branches and the bifurcations in modified non-smooth Chua's oscillator with slow-varying excitation,the bursting oscillations and the mechanism are presented.It is found that,though the pseudo-equilibrium points cannot be touched,it still affect the movement of the trajectory in the corresponding regions,which may result in different behaviors on the boundary,such as grazing and sliding phenomena.