Search results for "chaos"
showing 10 items of 106 documents
Chaos synchronization for a class of chaotic systems via H<inf>&#x221E;</inf> control technique
2013
In this paper, the robust synchronization control for a class of chaotic systems is studied. Based on linear matrix inequality techniques and Lyapunov stability theory, a novel H∝ robust synchronization controller is designed for the possible application in real engineering. Finally, some numerical simulations are included to demonstrate the effectiveness of the proposed techniques.
Impulsive control on the synchronization for a class of chaotic Systems
2014
In this paper, the impulsive control problem on the synchronization for a class of chaotic systems is discussed. Based on Lyapunov stability theory, the new impulsive synchronization strategy is presented to realize the chaos synchronization and possesses the wider scope of application. Finally the numerical simulation examples are given to demonstrate the effectiveness of our theoretical results.
Solving continuous models with dependent uncertainty: a computational approach
2013
This paper presents a computational study on a quasi-Galerkin projection-based method to deal with a class of systems of random ordinary differential equations (r.o.d.e.'s) which is assumed to depend on a finite number of random variables (r.v.'s). This class of systems of r.o.d.e.'s appears in different areas, particularly in epidemiology modelling. In contrast with the other available Galerkin-based techniques, such as the generalized Polynomial Chaos, the proposed method expands the solution directly in terms of the random inputs rather than auxiliary r.v.'s. Theoretically, Galerkin projection-based methods take advantage of orthogonality with the aim of simplifying the involved computat…
Dynamics, Operator Theory, and Infinite Holomorphy
2014
The works on linear dynamics in the last two decades show that many, even quite natural, linear dynamical systems exhibit wild behaviour. Linear chaos and hypercyclicity have been at the crossroads of several areas of mathematics. More recently, fascinating new connections have started to be explored: operators on spaces of analytic functions, semigroups and applications to partial differential equations, complex dynamics, and ergodic theory. Related aspects of functional analysis are the study of linear operators on Banach spaces by using geometric, topological, and algebraic techniques, the works on the geometry of Banach spaces and Banach algebras, and the study of the geometry of a Bana…
Memristors and nonequilibrium stochastic multistable systems
2022
The main aim of this special issue is to report the recent advances and new trends in memristors and nonequilibrium stochastic multistable systems, both theoretically and experimentally, within an interdisci-plinary context. In particular, memristors are multistable systems whose switching dynamics is a stochastic process, which can be controlled by internal and external noise sources, unveiling the constructive role of random fluctuations. Furthermore, the use of memristors as memory elements in neuromorphic systems with noise-assisted persistence of memory states, chaotic dynamics, metastable chaos and chaos synchronization, new stochastic nonlinear models, noise-induced phenomena such as…
Order and Chaos in the Statistical Mechanics of the Integrable Models in 1+1 Dimensions
1991
This paper was presented at the meeting under this title. But, originally, the more cumbersome ‘Quantum chaos — classical chaos in k-space: thermodynamic limits for the sine-Gordon models’ was proposed. Certainly this covers more technically the content of this paper.
Hidden attractors and multistability in a modified Chua’s circuit
2021
The first hidden chaotic attractor was discovered in a dimensionless piecewise-linear Chua’s system with a special Chua’s diode. But designing such physical Chua’s circuit is a challenging task due to the distinct slopes of Chua’s diode. In this paper, a modified Chua’s circuit is implemented using a 5-segment piecewise-linear Chua’s diode. In particular, the coexisting phenomena of hidden attractors and three point attractors are noticed in the entire period-doubling bifurcation route. Attraction basins of different coexisting attractors are explored. It is demonstrated that the hidden attractors have very small basins of attraction not being connected with any fixed point. The PSIM circui…
On lower-bound estimates of the Lyapunov dimension and topological entropy for the Rossler systems
2019
In this paper, on the example of the Rössler systems, the application of the Pyragas time-delay feedback control technique for verification of Eden’s conjecture on the maximum of local Lyapunov dimension, and for the estimation of the topological entropy is demonstrated. To this end, numerical experiments on computation of finite-time local Lyapunov dimensions and finite-time topological entropy on a Rössler attractor and embedded unstable periodic orbits are performed. The problem of reliable numerical computation of the mentioned dimension-like characteristics along the trajectories over large time intervals is discussed. peerReviewed
Quantum and Classical Statistical Mechanics of the Integrable Models in 1 + 1 Dimensions
1990
In a short but remarkable paper Yang and Yang [1] showed that the free energy of a model system consisting of N bosons on a line with repulsive δ-function interactions was given by a set of coupled integral equations. The Yangs’ chosen model is in fact the repulsive version of the quantum Nonlinear Schrodinger (NLS) model. We have shown that with appropriate extensions and different dispersion relations and phase shifts similar formulae apply to ‘all’ of the integrable models quantum or classical. These models include the sine-Gordon (s-G) and sinh-Gordon (sinh-G) models, the two NLS models (attractive and repulsive), the Landau-Lifshitz (L-L’) model which includes all four previous models,…
Constructing adaptive generalized polynomial chaos method to measure the uncertainty in continuous models: A computational approach
2015
Due to errors in measurements and inherent variability in the quantities of interest, models based on random differential equations give more realistic results than their deterministic counterpart. The generalized polynomial chaos (gPC) is a powerful technique used to approximate the solution of these equations when the random inputs follow standard probability distributions. But in many cases these random inputs do not have a standard probability distribution. In this paper, we present a step-by-step constructive methodology to implement directly a useful version of adaptive gPC for arbitrary distributions, extending the applicability of the gPC. The paper mainly focuses on the computation…