Modal synchronization of coupled bistable van der Pol oscillators

Shiroky, I.B.; Gendelman, Oleg

doi:10.1016/j.chaos.2020.110555

Cited by 5 publications

(1 citation statement)

References 26 publications

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“…Такой характер решения с позиций теории динамических систем не является положением равновесия или предельным циклом, что не позволяет применить численный аппарат теории продолжения решений нелинейных уравнений. Для преодоления этого затруднения был выполнен переход к новым переменным [10]:…”

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Differential resonant MEMS accelerometer: Synchronization characteristics of weakly coupled microbeam sensing elements

Indeitsev¹,

Igumnova²,

Лукин³

et al. 2023

Vestnik SPbSU. Mathematics. Mechanics. Astronomy

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This work is devoted to studying the conditions and scenarios for synchronizing oscillations of weakly coupled microbeam elements of a differential resonant MEMS accelerometer operating in the dual-loop self-oscillator mode. The model of a system of two Van der Pol self-oscillators with a nonlinear elastic coupling between moving elements, obtained using the Galerkin method, was studied using the multiscale method. The modes of beats and synchronization of oscillations of two resonators are found analytically and numerically, and the boundary between these modes in the space of system parameters is determined. Along with a local bifurcation analysis of the considered stationary regimes, a global analysis of the evolution and branching of limit cycles in the space of slow variables was also carried out, which made it possible to detect zones of coexistence of stable synchronization and beat regimes with their basins of attraction. The influence of the factor of the designed or technologically determined non-identity of the design of two resonators on the location of the parametric zones of synchronization and beats is studied.

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Differential resonant MEMS accelerometer: Synchronization characteristics of weakly coupled microbeam sensing elements

Indeitsev¹,

Igumnova²,

Лукин³

et al. 2023

Vestnik SPbSU. Mathematics. Mechanics. Astronomy

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Oscillatory systems with two degrees of freedom and van der Pol coupling: Analytical approach

Kraljevic,

Zukovic,

Cveticanin

2024

Math Methods in App Sciences

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In this paper steady‐state vibrations of the two‐degrees‐of‐freedom oscillatory systems with van der Pol coupling are investigated. The model is a system of two differential equations with weak nonlinearity. A new solving procedure based on D′Alembert's method and the method of time‐variable amplitude and phase is developed. The main advantage of the method in comparison to others is that it gives the solution of the system of two coupled weak nonlinear equations in the form that is simple to analyze, as it has the same form as the solution of the corresponding system of linear equations. In the paper two types of systems are considered: one, a two‐mass system with two degrees of freedom, and second, the one‐mass system with two degrees of freedom. The torsional vibrations of a two‐mass system and vibrations of a Jeffcott rotor with two‐degrees‐of‐freedom are analyzed. Analytically obtained results are numerically tested. It is obtained that the difference between analytic and numeric results is small and almost negligible. As the accuracy of the analytic solution is high, it is suitable for application in technics and engineering. Conclusions about steady‐state self‐sustainable oscillators, orbital, and limit cycle motions are given.

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Dynamic response and bifurcation for Rayleigh-Liénard oscillator under multiplicative colored noise

Yue¹,

Yu²,

Li³

et al. 2022

Chaos, Solitons & Fractals

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Modal synchronization of coupled bistable van der Pol oscillators

Cited by 5 publications

References 26 publications

Differential resonant MEMS accelerometer: Synchronization characteristics of weakly coupled microbeam sensing elements

Differential resonant MEMS accelerometer: Synchronization characteristics of weakly coupled microbeam sensing elements

Oscillatory systems with two degrees of freedom and van der Pol coupling: Analytical approach

Dynamic response and bifurcation for Rayleigh-Liénard oscillator under multiplicative colored noise

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