相关论文: A note on a piecewise-linear Duffing-type system

This study investigates the existence and stability of limit cycles resulting from self-excited oscillations in linear multi-degree-of-freedom systems subjected to discontinuous, state-dependent forcing. Using the method of averaging and…

The normal forms associated with holomorphic systems are well known in the literature. In this paper we are concerned about studying the piecewise smooth holomorphic systems (PWHS). Specifically, we classify the possible phase portraits of…

This paper studies the family of piecewise linear differential systems in the plane with two pieces separated by a cubic curve. By analyzing the obtained first order Melnikov function, we give an upper bound of the number of limit cycles…

This paper presents a criterion that provides an easy sufficient condition for a collection of line integrals to have the Chebyshev property. The condition is based on the functions appearing in the line integrals. The criterion is used to…

We consider a many-parametric piecewise mapping with discontinuity. That is a one dimensional model of singular dynamic system. The stability boundary are calculated analytically and numerically. New typical features of stable cycle…

We consider a class of continuous-time hybrid dynamical systems that correspond to subgradient flows of a piecewise linear and convex potential function with finitely many pieces, and which include the fluid-level dynamics of the Max-Weight…

In this article, we study a model of random permutations, which we call random standardized permutations, based on a sequence of i.i.d. random variables. This model generalizes others, such as the riffle-shuffle and the major-index-biased…

For many physical systems the transition from a stationary solution to sustained small amplitude oscillations corresponds to a Hopf bifurcation. For systems involving impacts, thresholds, switches, or other abrupt events, however, this…

We study the dynamics of a mechanical oscillator with linear and cubic forces -the Duffing oscillator- subject to a feedback mechanism that allows the system to sustain autonomous periodic motion with well-defined amplitude and frequency.…

Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…

We introduce a versatile class of prototype dynamical systems for the study of complex bifurcation cascades of limit cycles, including bifurcations breaking spontaneously a symmetry of the system, period doubling bifurcations and…

We develop a convergent variational perturbation theory for the frequency of time-periodic solutions of nonlinear dynamical systems. The power of the theory is illustrated by applying it to the Duffing oscillator.

We report on an ultra-high-frequency (> 1 GHz), piecewise-linear chaotic system designed from low-cost, commercially available electronic components. The system is composed of two electronic time-delayed feedback loops: A primary analog…

We consider spin systems between a finite number $N$ of "species" or "phases" partitioning a cubic lattice $\mathbb{Z}^d$. We suppose that interactions between points of the same phase are coercive, while between point of different phases…

Using the predictor-corrector scheme, the fractional order diffusionless Lorenz system is investigated numerically. The effective chaotic range of the fractional order diffusionless system for variation of the single control parameter is…

For non-equilibrium systems described by finite Markov processes, we consider the number of times that a system traverses a cyclic sequence of states (a cycle). The joint distribution of the number of forward and backward instances of any…

A new systematic approach to the construction of approximate solutions to a class of nonlinear singularly perturbed feedback control systems using the boundary layer functions especially with regard to the possible occurrence of the…

Nonlinear dynamics of a bouncing ball moving vertically in a gravitational field and colliding with a moving limiter is considered and the Poincare map, describing evolution from an impact to the next impact, is described. Displacement of…

We explore phenomenological consequences of coupling a non-conformal scale-invariant theory to the standard model. We point out that, under certain circumstances, non-conformal scale-invariant theories have oscillating correlation functions…

An analysis of stick-slip behavior and convergence of trajectories in the feedback-controlled motion systems with discontinuous Coulomb friction is provided. A closed-form parameter-dependent stiction region, around an invariant equilibrium…