Search results for "Van der Pol oscillator"

A minimal limit-cycle model to profile movement patterns of individuals during agility drill performance: Effects of skill level.

2015

Identification of control strategies during agility performance is significant in understanding movement behavior. This study aimed at providing a fundamental mathematical model for describing the motion of participants during an agility drill and to determine whether skill level constrained model components. Motion patterns of two groups of skilled and unskilled participants (n = 8 in each) during performance of a forward/backward agility drill modeled as limit-cycles. Participant movements were recorded by motion capture of a reflective marker attached to the sacrum of each individual. Graphical and regression analyses of movement kinematics in Hooke’s plane, phase plane and velocity prof…

Coherence resonance in Bonhoeffer-Van der Pol circuit

2009

International audience; A nonlinear electronic circuit simulating the neuronal activity in a noisy environment is proposed. This electronic circuit is exactly ruled by the set of Bonhoeffer-Van Der Pol equations and is excited with a Gaussian noise. Without external deterministic stimuli, it is shown that the circuit exhibits the so-called 'coherence resonance' phenomenon.

Path Integral approach via Laplace’s method of integration for nonstationary response of nonlinear systems

2019

In this paper the nonstationary response of a class of nonlinear systems subject to broad-band stochastic excitations is examined. A version of the Path Integral (PI) approach is developed for determining the evolution of the response probability density function (PDF). Specifically, the PI approach, utilized for evaluating the response PDF in short time steps based on the Chapman–Kolmogorov equation, is here employed in conjunction with the Laplace’s method of integration. In this manner, an approximate analytical solution of the integral involved in this equation is obtained, thus circumventing the repetitive integrations generally required in the conventional numerical implementation of …

Noise-induced transitions in a stochastic Goodwin-type business cycle model

2017

Abstract We motivate and specify a stochastic Goodwin-type business cycle model. Our analysis focusses on a subset of the parameter space where several attractors coexist. Applying a semi-numerical approach based on the stochastic sensitivity function and confidence domains due to Milstein and Ryashko (1995) , we study random transitions between stable attractors in the context of the Goodwin-type economy embedded in an uncertain environment. Relying on a mix of analytical considerations and simulations we demonstrate that under weak noise levels regime switching is a prominent feature in the presence of low saving rates. Moreover, we explain how increased uncertainty can induce an essentia…

Mixed-mode oscillation-incrementing bifurcations and a devil’s staircase from a nonautonomous, constrained Bonhoeffer-van der Pol oscillator

2018

General Linearized Theory of Quantum Fluctuations around Arbitrary Limit Cycles

2017

The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its accuracy far from critical points or situations where the nonlinearity reaches the strong coupling regime, has turned it into a widespread technique, which is the first method of choice in most works on the subject. However, such a technique finds strong practical and conceptual complications when one tries to apply it to situations in which the classical long-time solution is time dependent, a most prominent example being spontaneous limit-cycle formation. H…

Nonstationary response envelope probability densities of nonlinear oscillators

2006

The nonstationary random response of a class of lightly damped nonlinear oscillators subjected to Gaussian white noise is considered. An approximate analytical method for determining the response envelope statistics is presented. Within the framework of stochastic averaging, the procedure relies on the Markovian modeling of the response envelope process through the definition of an equivalent linear system with response-dependent parameters. An approximate solution of the associated Fokker-Planck equation is derived by resorting to a Galerkin scheme. Specifically, the nonstationary probability density function of the response envelope is expressed as the sum of a time-dependent Rayleigh dis…