Search results for "Chaotic"
showing 10 items of 297 documents
Classical wave thermalisation in chaotic multimode optical fibre
2023
Vibrating and shaking soliton pairs in dissipative systems
2007
We show that two-soliton solutions in nonlinear dissipative systems can exist in various forms. As with single solitons, they can be stationary, periodic or chaotic. In particular, we find new types of vibrating and shaking soliton pairs. Each type of pair is stable in the sense that the bound state exists in the same form indefinitely. © 2006 Elsevier B.V. All rights reserved.
In vitro simulation of spiral waves in cardiomyocyte networks using multi-electrode array technology
2009
International audience; We aimed thus to provide new insights into the cellular origin of the fibrillation phenomenon by exploring the impulse propagation between cardiac myocytes in confluent monolayers of cultured cardiomyocytes (CM),
Complex behavior of ray in gaussian index profile periodicaly segmented waveguide
2006
International audience; In this article, we present a numerical analysis concerning ray propagation in a multimode periodic segmented waveguide with a gaussian index segment profile. We show that this simple waveguide configuration exhibits a complex ray dynamics that can be regular or chaotic depending on the initial conditions.
Global linear feedback control for the generalized Lorenz system
2006
Abstract In this paper we show how the chaotic behavior of the Chen system can be controlled via feedback technique. We design both a nonlinear feedback controller and a linear one which globally regulate the closed-loop system states to a given point. We finally show that our approach works also for the whole family of the generalized Lorenz system.
Time-delay control for stabilization of the Shapovalov mid-size firm model
2020
Control and stabilization of irregular and unstable behavior of dynamic systems (including chaotic processes) are interdisciplinary problems of interest to a variety of scientific fields and applications. Using the control methods allows improvements in forecasting the dynamics of unstable economic processes and offers opportunities for governments, central banks, and other policy makers to modify the behaviour of the economic system to achieve its best performance. One effective method for control of chaos and computation of unstable periodic orbits (UPOs) is the unstable delay feedback control (UDFC) approach, suggested by K. Pyragas. This paper proposes the application of the Pyragas' me…
D3 Dihedral Logistic Map of Fractional Order
2021
In this paper, the D3 dihedral logistic map of fractional order is introduced. The map presents a dihedral symmetry D3. It is numerically shown that the construction and interpretation of the bifurcation diagram versus the fractional order requires special attention. The system stability is determined and the problem of hidden attractors is analyzed. Furthermore, analytical and numerical results show that the chaotic attractor of integer order, with D3 symmetries, looses its symmetry in the fractional-order variant.
The Lorenz system : hidden boundary of practical stability and the Lyapunov dimension
2020
On the example of the famous Lorenz system, the difficulties and opportunities of reliable numerical analysis of chaotic dynamical systems are discussed in this article. For the Lorenz system, the boundaries of global stability are estimated and the difficulties of numerically studying the birth of self-excited and hidden attractors, caused by the loss of global stability, are discussed. The problem of reliable numerical computation of the finite-time Lyapunov dimension along the trajectories over large time intervals is discussed. Estimating the Lyapunov dimension of attractors via the Pyragas time-delayed feedback control technique and the Leonov method is demonstrated. Taking into accoun…
Complex dynamics, hidden attractors and continuous approximation of a fractional-order hyperchaotic PWC system
2018
In this paper, a continuous approximation to studying a class of PWC systems of fractionalorder is presented. Some known results of set-valued analysis and differential inclusions are utilized. The example of a hyperchaotic PWC system of fractional order is analyzed. It is found that without equilibria, the system has hidden attractors.