Related papers: Analysis of a Parametrically Driven Pendulum
In this work, we analyzed theoretically and experimentally the nonlinear dynamics of a magnetic pendulum driven by a coil-magnet interaction. The force between the magnetic elements and the resulting torque on the pendulum are derived using…
Nonholonomic systems are variational models commonly used for mechanical systems with ideal no-slip constraints. This note provides a differential-geometric derivation of the nonholonomic equations of motion for an arbitrary rigid body…
We study the asymptotics, box dimension, and Minkowski content of trajectories of some discrete dynamical systems. We show that under very general conditions, trajectories corresponding to parameters where saddle-node bifurcation appears…
Symbolic models are abstract descriptions of continuous systems in which symbols represent aggregates of continuous states. In the last few years there has been a growing interest in the use of symbolic models as a tool for mitigating…
Symbolic dynamics, which partitions an infinite number of finite-length trajectories into a finite number of trajectory sets, describes the dynamics of a system in a simplified and coarse-grained way with a limited number of symbols. The…
In this paper, we consider sufficient conditions for an invariant double circle to occur in a one parameter discrete dynamical systems on a cylinder.
We study two-dimensional, two-piece, piecewise-linear maps having two saddle fixed points. Such maps reduce to a four-parameter family and are well known to have a chaotic attractor throughout open regions of parameter space. The purpose of…
For a model nonlinear dynamical system, we show how one may obtain its bifurcation behavior by introducing noise into the dynamics and then studying the resulting Langevin dynamics in the weak-noise limit. A suitable quantity to capture the…
We theoretically study the dynamics of a pair of coupled pendulums subject to a periodic temporal modulation of their oscillation frequency. Inspired from analogous developments in quantum mechanics, we anticipate dynamical localization and…
This paper presents a rigorous analytical model of traffic dynamics on a circular track, demonstrating the emergence of standing oscillations resulting from microscopic driver behaviour, delay responses, and proximity pressure. Without…
We consider a damped magnetic oscillator, consisting of a permanent magnet in a periodically oscillating magnetic field. A detailed investigation of the dynamics of this dissipative magnetic system is made by varying the field amplitude…
Detecting regime shifts in chaotic time series is hard because observation-space signals are entangled with intrinsic variability. We propose Parameter--Space Changepoint Detection (Param--CPD), a two--stage framework that first amortizes…
Using extensive particle-based simulations, we investigate out-of-equilibrium pattern dynamics in an oppositely driven binary particle system in two dimensions. A surprisingly rich dynamical behavior including lane formation, jamming,…
For studying the objectivity and the quality of a given form of the Periodic system as a single whole we compare plots of functions presenting properties of elements in pairs of periods. Using mathematical statistics we introduce a…
The appearance of infinitely-many period-doubling cascades is one of the most prominent features observed in the study of maps depending on a parameter. They are associated with chaotic behavior, since bifurcation diagrams of a map with a…
We investigate the quantum recurrence phenomena in periodically driven systems. We calculate the classical period and the quantum recurrence time and develop their interdependence. We further predict the behavior of the recurrence phenomena…
Periodically driven flows are fundamental models of chaotic behavior and the study of their transport properties is an active area of research. A well-known analytic construction is the augmentation of phase space with an additional time…
The quantum mechanical equivalent of parametric resonance is studied. A simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly. Classically stable and unstable regions in parameter space are…
Circadian rhythms are archetypical examples of nonlinear oscillations. While these oscillations are usually attributed to circuits of biochemical interactions among clock genes and proteins, recent experimental studies reveal that they are…
The mathematical model representing the equation of motion of a pendulum is nonlinear. Solutions that satisfy the equation cannot be represented by elementary functions, such as trigonometric functions. To solve such problems, it is common…