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Two novel bursting patterns in the Duffing system with multiple-frequency slow parametric excitations
Xiujing Han1, Yi Zhang1, Qinsheng Bi1
1Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, People's Republic of China.
Chaos (Woodbury, N.Y.)
|January 8, 2020
Summary
This study reveals two new bursting patterns in the Duffing system: turnover-of-pitchfork-hysteresis-induced bursting and compound pitchfork-hysteresis bursting, driven by multiple-frequency parametric excitations.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Mathematical Physics
Background:
- The Duffing system is a fundamental model in nonlinear dynamics.
- Hysteresis phenomena, particularly those induced by pitchfork bifurcations, are crucial for understanding complex system behaviors.
- Delayed bifurcations can lead to intricate dynamic patterns.
Purpose of the Study:
- To identify and characterize novel bursting patterns in a parametrically excited Duffing system.
- To investigate the mechanisms behind these new bursting patterns, specifically focusing on pitchfork bifurcations and hysteresis.
- To analyze the influence of system parameters on the emergence and characteristics of these novel dynamics.
Main Methods:
- Numerical analysis of the Duffing oscillator under multiple-frequency parametric excitations.
- Investigation of pitchfork bifurcations and delay-induced hysteresis in the fast subsystem.
- Systematic exploration of parameter spaces to reveal novel bursting behaviors.
Main Results:
- Discovery of two new bursting patterns: turnover-of-pitchfork-hysteresis-induced bursting and compound pitchfork-hysteresis bursting.
- Demonstration that stable equilibrium branches can exhibit complex, winding trajectories leading to novel bursting.
- Identification of conditions for additional pitchfork bifurcations, enabling multiple hysteresis loops and compound bursting.
Conclusions:
- The Duffing system with multiple-frequency parametric excitations exhibits complex dynamics, including novel bursting patterns.
- Pitchfork bifurcations and resulting hysteresis play a critical role in generating these complex bursting behaviors.
- Parameter variations significantly influence the occurrence and nature of these discovered bursting patterns.
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