Systematic designing of bi-rhythmic and tri-rhythmic models in families of Van der Pol and Rayleigh oscillators
DOI10.1016/j.cnsns.2020.105234zbMath1457.34029arXiv2008.03499OpenAlexW3006069624MaRDI QIDQ2204512
Sandip Saha, Gautam Gangopadhyay, Deb Shankar Ray
Publication date: 15 October 2020
Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2008.03499
limit cycleRayleigh oscillatorVan der Pol oscillatorLiénard-Levinson-Smith oscillatorbi-rhythmic and tri-rhythmic oscillators
Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear ordinary differential equations and systems (34A34) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)
Cites Work
- Control of multistability
- Self-oscillation
- Reduction of kinetic equations to Liénard-Levinson-Smith form: counting limit cycles
- Estimating the boundaries of a limit cycle in a 2D dynamical system using renormalization group
- Isochronicity and limit cycle oscillation in chemical systems
- Parametrically excited non-linearity in Van der Pol oscillator: resonance, anti-resonance and switch
- A general equation for relaxation oscillations
- Transformation theory of non-linear differential equations of the second order
- Multistationarity, the basis of cell differentiation and memory. I. Structural conditions of multistationarity and other nontrivial behavior
- The number of small-amplitude limit cycles of Liénard equations
- DYNAMICS AND ACTIVE CONTROL OF MOTION OF A DRIVEN MULTI-LIMIT-CYCLE VAN DER POL OSCILLATOR
- Synchronization of two coupled self-excited systems with multi-limit cycles
- Birhythmicity, chaos, and other patterns of temporal self-organization in a multiply regulated biochemical system.
- BIFURCATION STRUCTURE OF A DRIVEN, MULTI-LIMIT-CYCLE VAN DER POL OSCILLATOR (I): THE SUPERHARMONIC RESONANCE STRUCTURE
- Dissipative structures in biological systems: bistability, oscillations, spatial patterns and waves
- Control of birhythmicity: A self-feedback approach
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