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The Duffing oscillator is a paradigm of bistable oscillatory motion in physics, engineering, and biology. Time series of such oscillations are often observed experimentally in a nonlinear system excited by a spontaneously fluctuating force.…
This paper considers the oscillations modeled by a forced Van der Pol generalized oscillator. These oscillations are described by a nonlinear differential equation of the form $…
Daylight plays a major role in the wake/sleep cycle in humans. Indeed, the wake/sleep system stems from biological systems that follow a circadian rhythm determined by the light/dark alternation. The oscillations can be modeled by the…
Nonlinear oscillators are commonly encountered in a wide range of physical and engineering systems, exhibiting rich and complex dynamics. Among these, the Van der Pol oscillator is well known for its self-sustained limit cycle behavior.…
In this paper, Van der pol equation has been analyzed for stability and bifurcation phenomena with and without forcing component. Analytical solution of the Van der pol equation using Method of Multiple Scales (MMS) is compared with…
This paper considers nonlinear dynamics of plasma oscillations modeled by a forced modified Van der Pol-Duffing oscillator. These plasma oscillations are described by a nonlinear differential equation of the form $ \ddot{x}+ \epsilon (1…
Theoretical models that describe oscillations in biological systems are often either a limit cycle oscillator, where the deterministic nonlinear dynamics gives sustained periodic oscillations, or a noise-induced oscillator, where a fixed…
This study focuses on extending the concept of weak signal enhancement from dynamical systems based on vibrational resonance of nonlinear systems, to non-smooth systems. A Van der Pol- Duffing oscillator with a one-sided barrier, subjected…
Nonlinear systems play a significant role in numerous scientific and engineering disciplines, and comprehending their behavior is crucial for the development of effective control and prediction strategies. This paper introduces a novel…
A van der Pol self sustained oscillator with higher order nonlinearity exhibits a rich dynamics, with multiple periodic attractors, and still the model allows analytical approximations. Some of these properties can be conveniently exploited…
We present a model-based, output-only parameter identification method for self-sustained oscillators forced by dynamic noise, which we illustrate experimentally with an aeroacoustic setup: a turbulent jet impinging a beer bottle and…
The equation of the Van der Pol oscillator, being characterized by a dissipative term, is non-Lagrangian. Appending an additional degree of freedom we bring the equation in the frame of action principle and thus introduce a one-way coupled…
Nonlinear oscillators are a key modelling tool in many applications. The influence of annealed noise on nonlinear oscillators has been studied intensively. It can induce effects in nonlinear oscillators not present in the deterministic…
In this work, we present the basic theoretical efforts that are known in order to deal with non-trivial solutions of the Van der Pol oscillator, such as theory of average, successive approximations and symbolic dynamics. We also construct a…
A noisy damping parameter in the equation of motion of a nonlinear oscillator renders the fixed point of the system unstable when the amplitude of the noise is sufficiently large. However, the stability diagram of the system can not be…
We address the distinction between dynamical and additive noise in time series analysis by making a joint evaluation of both the statistical continuity of the series and the statistical differentiability of the reconstructed measure. Low…
We outline formal and physical similarities between the quantum dynamics of open systems, and the mesoscopic description of classical systems affected by weak noise. The main tool of our interest is the dissipative Wigner equation, that,…
Networks of coupled nonlinear oscillators model a broad class of physical, chemical and biological systems. Understanding emergent patterns in such networks is an ongoing effort with profound implications for different fields. In this work,…
Laser resonances play a crucial role in optical and quantum systems because the photons impact the stability and coherence of laser sources. While laser oscillations are typically stable and periodic, the presence of nonlinear effects can…
We investigate the effects of exponentially correlated noise on birhythmic van der Pol type oscillators. The analytical results are obtained applying the quasi-harmonic assumption to the Langevin equation to derive an approximated…