Related papers: Localization of hidden Chua attractors by the desc…
The coupled Stuart-Landau equation serves as a fundamental model for exploring synchronization and emergent behavior in complex dynamical systems. However, understanding its dynamics from a comprehensive nonlinear perspective remains…
The growth in number and nature of dynamical attractors in Kauffman NK network models are still not well understood properties of these important random boolean networks. Structural circuits in the underpinning graph give insights into the…
Localized vibrations, arising from nonlinearities or symmetry breaking, pose a challenge in engineering, as the resulting high-amplitude vibrations may result in component failure due to fatigue. During operation, the emergence of…
We propose a simple and new unified method to achieve lag, complete and anticipatory synchronizations in coupled nonlinear systems. It can be considered as an alternative to the subsystem and intentional parameter mismatch methods. This…
The paper presents the method of attractive cylinders -- a generalization of the atrractive ellipsoid method to the cases of tracking and observation. Based on the developed method, an algorithm for calculating the parameters of the…
We present a control scheme that is able to find and stabilize an unstable chaotic regime in a system with a large number of interacting particles. This allows us to track a high dimensional chaotic attractor through a bifurcation where it…
Given a family of systems, identifying stabilizing switching signals in terms of infinite walks constructed by concatenating cycles on the underlying directed graph of a switched system that satisfy certain conditions, is a well-known…
Unstable Periodic Orbits (UPOs) were used to identify regimes, and transitions between regimes, in a reduced-order coupled atmosphere-land spectral model. In this paper we describe how the chaotic attractor of this model was clustered using…
The paper develops new sufficient conditions for synchronization of a network of $N$ nonlinearly coupled Chua oscillators interconnected via the first state coordinate only. The nonlinear coupling strength is governed by a function residing…
We consider the set-point control problem for nonlinear systems with flat output that are subject to perturbations. The nonlinear dynamics as well as the perturbations are locally Lipschitz. We apply the model-following control (MFC)…
The structure of the Lorenz-84 attractor is investigated in this study. Its dynamics belonging to weakly dissipative chaos, classical approaches cannot be used to analyze its structure. The color tracer mapping is introduced for this…
In this article we introduce an original model in order to study the emergence of chaos in a reaction diffusion system in the presence of self- and cross-diffusion terms. A Fourier Spectral Method is derived to approximate equilibria and…
Investigating the possibility of applying techniques from linear systems theory to the setting of nonlinear systems has been the focus of many papers. The pseudo linear form representation of nonlinear dynamical systems has led to the…
Recent studies show indication of the effectiveness of synchronization as a data assimilation tool for small or meso-scale forecast when less number of variables are observed frequently. Our main aim here is to understand the effects of…
An attractor of a piecewise-smooth continuous system of differential equations can bifurcate from a stable equilibrium to a more complicated invariant set when it collides with a switching manifold under parameter variation. Here numerical…
We made the chaotic circuit proposed by Chua and the memristic circuit proposed by Muthuswamy and Chua, and analyzed the behavior of the voltage of the capacitor, electric current in the inductor and the voltage of the memristor by adding…
We study the dynamical regimes that emerge from the strongly coupling between two Chua's circuits with parameters mismatch. For the region around the perfect synchronous state we show how to combine parameter diversity and coupling in order…
Attractors of cooperative dynamical systems are particularly simple; for example, a nontrivial periodic orbit cannot be an attractor. This paper provides characterizations of attractors for the wider class of coherent systems, defined by…
The initial boundary value problem for a nonlinear system of equations modeling the chevron patterns is studied in one and two spatial dimensions. The existence of an exponential attractor and the stabilization of the zero steady state…
The focus of this paper is on linear system identification in the setting where it is known that the underlying partially-observed linear dynamical system lies within a finite collection of known candidate models. We first consider the…