Related papers: Systematic experimental exploration of bifurcation…
Consider a dynamical system given by a planar differential equation, which exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is known that under random perturbations, the distribution of locations where the…
Nonlinear control-affine systems described by ordinary differential equations with bounded measurable input functions are considered. The solvability of general boundary value problems for these systems is formulated in the sense of…
We outline a general theory for the analysis of flow-distributed standing and travelling wave patterns in one-dimensional, open plug-flows of oscillatory chemical media. We treat both the amplitude and phase dynamics of small and…
In this manuscript, an original numerical procedure for the nonlinear peridynamics on arbitrarily--shaped two-dimensional (2D) closed manifolds is proposed. When dealing with non parameterized 2D manifolds at the discrete scale, the problem…
In this paper, we will consider a class of continuous-time stochastic control systems with both unknown nonlinear structure and unknown disturbances, and investigate the capability of the classical proportional-integral-derivative(PID)…
We experimentally implement a virtual geometric periodicity in an elastic metamaterial. First, unwanted boundary reflections at the domain ends are cancelled through the iterative injection of the polarity reversed, reflected wavefield. The…
An approach to stabilization of control systems with ultimately wide ranges of uncertainly disturbed parameters is offered. The method relies on using of nonlinear structurally stable functions from catastrophe theory as controllers.…
Optomechanical coupling between the motion of a mechanical oscillator and a cavity represents a new arena for experimental investigation of quantum effects on the mesoscopic and macroscopic scale.The motional sidebands of the output of a…
Nonstationary and nonlinear signals are ubiquitous in real life. Their decomposition and analysis is an important topic of research in signal processing. Recently a new technique, called Iterative Filtering, has been developed with the goal…
For many years it was believed that an unstable periodic orbit with an odd number of real Floquet multipliers greater than unity cannot be stabilized by the time-delayed feedback control mechanism of Pyragus. A recent paper by Fiedler et al…
Nonlinear extension of the integral part of a standard proportional-integral-derivative (PID) feedback control is proposed for perturbed second-order systems. The approach is model-free and requires solely the Lipschitz boundedness of the…
Hidden attractors are present in many nonlinear dynamical systems and are not associated with equilibria, making them difficult to locate. Recent studies have demonstrated methods of locating hidden attractors, but the route to these…
This paper proposes a novel direct adaptive control method for rejecting unknown deterministic disturbances and tracking unknown trajectories in systems with uncertain dynamics when the disturbances or trajectories are the summation of…
The effective, fast transport of matter through porous media is often characterized by complex dispersion effects. To describe in mathematical terms such situations, instead of a simple macroscopic equation (as in the classical Darcy's…
We study the pattern of activated trajectories in a double well system without detailed balance, in the weak noise limit. The pattern may contain cusps and other singular features, which are similar to the caustics of geometrical optics.…
This paper focuses on the invariance control problem for discrete-time switched nonlinear systems. The proposed approach computes controlled invariant sets in a finite number of iterations and directly yields a partition-based invariance…
We report on the possibilities of using the method of normal fundamental systems for solving some problems of oscillation theory. Large elastic dynamical systems with continuous and discrete parameters are considered, which have many…
Nonlinear spin systems exhibit rich and exotic dynamical phenomena, offering promising applications ranging from spin masers and time crystals to precision measurement. Recent theoretical work [T. Wang et al., Commun. Phys. 8, 41 (2025)]…
Vector fields that are discontinuous on codimension-one surfaces are known as Filippov systems and can have attracting periodic orbits involving segments that are contained on a discontinuity surface of the vector field. In this paper we…
We study three different experiments that involve dry friction and periodic driving, and which employ both single and many-particle systems. These experimental set-ups, besides providing a playground for investigation of frictional effects,…