Routes to bursting oscillations in a modified van der Pol–Duffing oscillator with slow-varying periodic excitation

2017 ◽  
pp. 107754631774002 ◽  
Author(s):  
Ma Xindong ◽  
Cao Shuqian ◽  
Guo Hulun
Keyword(s):  
Duffing Oscillator ◽  
Periodic Excitation ◽  
Van Der Pol ◽  
Bursting Oscillations

Complex Bursting Patterns in a van der Pol–Mathieu–Duffing Oscillator

2021 ◽  
Vol 31 (06) ◽  
pp. 2150082
Author(s):  
Xindong Ma ◽  
Jin Song ◽  
Mengke Wei ◽  
Xiujing Han ◽  
Qinsheng Bi
Keyword(s):  
Duffing Oscillator ◽  
Relaxation Oscillation ◽  
Multiple Frequency ◽  
Van Der Pol ◽  
Bursting Oscillations ◽  
Duffing System ◽  
Dynamical Behaviors ◽  
Parameter Interval ◽  
Bursting Oscillation

The pulse-shaped explosion (PSE), characterized by the pulse-shaped quantitative of system solutions varying dramatically, is a special route to bursting oscillations reported recently. This paper reports interesting dynamical behaviors related to the PSE of equilibria, and based on that, the complex bursting dynamics is investigated in a van der Pol–Mathieu–Duffing system with multiple-frequency slow-varying excitations. We find that bifurcations can be observed in a narrow parameter interval within PSE. We also show that two groups of bifurcations are symmetrically arranged on both sides of PSE, and each of which determines a different bursting part. Based on this, two compound bursting patterns, i.e. compound Hopf/Hopf bursting oscillation and compound subHopf/fold cycle bursting oscillation, and a novel type of relaxation oscillation (bursting oscillation of point/point) independent of bifurcations, are revealed. Our results enrich the knowledge of dynamical behaviors related to PSE as well as the possible routes to complex bursting dynamics.

scholarly journals Bursting Oscillation and Its Mechanism of a Generalized Duffing–Van der Pol System with Periodic Excitation

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Youhua Qian ◽  
Danjin Zhang ◽  
Bingwen Lin
Keyword(s):  
Numerical Simulations ◽  
Phase Portrait ◽  
Time Scales ◽  
Bifurcation Analysis ◽  
Hot Spot ◽  
Periodic Excitation ◽  
Fast Subsystem ◽  
Van Der Pol ◽  
Bursting Oscillations ◽  
Bursting Oscillation

The complex bursting oscillation and bifurcation mechanisms in coupling systems of different scales have been a hot spot domestically and overseas. In this paper, we analyze the bursting oscillation of a generalized Duffing–Van der Pol system with periodic excitation. Regarding this periodic excitation as a slow-varying parameter, the system can possess two time scales and the equilibrium curves and bifurcation analysis of the fast subsystem with slow-varying parameters are given. Through numerical simulations, we obtain four kinds of typical bursting oscillations, namely, symmetric fold/fold bursting, symmetric fold/supHopf bursting, symmetric subHopf/fold cycle bursting, and symmetric subHopf/subHopf bursting. It is found that these four kinds of bursting oscillations are symmetric. Combining the transformed phase portrait with bifurcation analysis, we can observe bursting oscillations obviously and further reveal bifurcation mechanisms of these four kinds of bursting oscillations.

scholarly journals Hyperchaos and bifurcations in a driven Van der Pol–Duffing oscillator circuit

2014 ◽  
Vol 3 (4) ◽  
pp. 363-370 ◽  
Author(s):  
U. E. Vincent ◽  
B. R. Nana Nbendjo ◽  
A. A. Ajayi ◽  
A. N. Njah ◽  
P. V. E. McClintock
Keyword(s):  
Duffing Oscillator ◽  
Van Der Pol ◽  
Oscillator Circuit

Observe-Based Projective Synchronization of Chaotic Complex Modified Van Der Pol-Duffing Oscillator With Application to Secure Communication

2015 ◽  
Vol 10 (5) ◽  
Author(s):  
Ping Liu ◽  
Hongjun Song ◽  
Xiang Li
Keyword(s):  
Secure Communication ◽  
Chaotic Behavior ◽  
Design Method ◽  
Duffing Oscillator ◽  
Scaling Factor ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Projective Synchronization ◽  
Chaotic Oscillator ◽  
Van Der Pol

This paper addresses the projective synchronization (PS) of the complex modified Van der Pol-Duffing (MVDPD for short) chaotic oscillator by using the nonlinear observer control and also discusses its applications to secure communication in theory. First, we construct the complex MVDPD oscillator and analysis its chaotic behavior. Moreover, an observer design method is applied to achieve PS of two identical MVDPD chaotic oscillators with complex offset terms, which are synchronized to the desired scale factor. The unpredictability of the scaling factor could further enhance the security of the communication. Finally, numerical simulations are given to demonstrate the effectiveness and feasibility of the proposed synchronization approach and also verify the success application to the proposed scheme’s in the secure communication.

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