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We develop a contraction-based framework to establish the existence and exponential stability of periodic solutions in planar nonsmooth dynamical systems governed by Filippov differential inclusions. The method integrates a time- and…
The dynamics of a non-autonomous oscillator in which the phase and frequency of the external force depend on the dynamical variable is studied. Such a control of the phase and frequency of the external force leads to the appearance of…
We consider a periodically-forced 1-D Langevin equation that possesses two stable periodic solutions in the absence of noise. We ask the question: is there a most likely noise-induced transition path between these periodic solutions that…
Systems of dynamical elements exhibiting spontaneous rhythms are found in various fields of science and engineering, including physics, chemistry, biology, physiology, and mechanical and electrical engineering. Such dynamical elements are…
We examine some nontrivial consequences that emerge from interpreting a position-dependent mass (PDM) driven Duffing oscillator in the presence of a quartic potential. The propagation dynamics is studied numerically and sensi- tivity to the…
The paper deals with electromagnetic perturbations of a central force problem of the form \begin{equation*} \dfrac{\mathrm{d}}{\mathrm{d}t} \bigl( \varphi(\dot{x}) \bigr) = V'(|x|) \dfrac{x}{|x|} + E_{\varepsilon}(t,x)+\dot{x} \wedge…
The paper suggests a preconditioning type method for fast solving of elliptic equations with oscillating quasiperiodic coefficients $A_\epsilon$ specified by the small parameter $\epsilon>0$. We use an iteration method generated by an…
The stationary and highly non-stationary resonant dynamics of the harmonically forced pendulum are described in the framework of a semi-inverse procedure combined with the Limiting Phase Trajectory concept. This procedure, implying only…
Phase control of parametric modulation in coupled oscillator networks enables sculpting of dynamical states with desired spatiotemporal symmetries. Symmetry-aware Floquet analysis successfully predicts such states in linear systems, but…
This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…
We contribute to the method of trigonometric series for solving differential equations of certain non linear oscillators. Key Words: series power solution, trigonometric series.
A classical double oscillator model, that includes in certain parameter limits, the standard harmonic oscillator and the inverse oscillator, is interpreted as a dynamical system. We study its essential features and make a qualitative…
We introduce a class of convex, higher-dimensional billiard models which generalise stadium billiards. These models correspond to the free motion of a point-particle in a region bounded by cylinders cut by planes. They are motivated by…
We review some recent results surrounding a general mechanism for producing chaotic behavior in periodically-kicked oscillators. The key geometric ideas are illustrated via a simple linear shear model.
Nonlinear isolated and coupled oscillators are extensively studied as prototypical nonlinear dynamics models. Much attention has been devoted to oscillator synchronization or the lack thereof. Here, we study the synchronization and…
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.…
Response solutions are quasi-periodic ones with the same frequency as the forcing term. The present work is devoted to constructing response solutions for $d$-dimensional nonlinear plate models with nonlocal energy damping, which are…
We propose a method for designing two-dimensional limit-cycle oscillators with prescribed periodic trajectories and phase response properties based on the phase reduction theory, which gives a concise description of weakly-perturbed…
In this report, we address differential systems with Lipschitz non linearities; this study is motivated by the subject of vibrations of structures with unilateral springs or non linear stress-strain law close to the linear case. We consider…
The Van der Pol equation is a paradigmatic model of relaxation oscillations. This remarkable nonlinear phenomenon of self-sustained oscillatory motion underlies important rhythmic processes in nature and electrical engineering. Relaxation…