Search results for "chaos"
showing 10 items of 106 documents
Robust Adaptive H∞ Synchronization of Master-Slave Systems with Discrete and Distributed Time-Varying Delays and Nonlinear Perturbations
2011
Author's version of a chapter published in the book: Proceedings of the 18th IFAC World Congress 2011. Also available from the publisher at: http://dx.doi.org/10.3182/20110828-6-IT-1002.03116
Hidden attractors on one path : Glukhovsky-Dolzhansky, Lorenz, and Rabinovich systems
2017
In this report, by the numerical continuation method we visualize and connect hidden chaotic sets in the Glukhovsky-Dolzhansky, Lorenz and Rabinovich systems using a certain path in the parameter space of a Lorenz-like system.
Looking More Closely at the Rabinovich-Fabrikant System
2016
Recently, we looked more closely into the Rabinovich–Fabrikant system, after a decade of study [Danca & Chen, 2004], discovering some new characteristics such as cycling chaos, transient chaos, chaotic hidden attractors and a new kind of saddle-like attractor. In addition to extensive and accurate numerical analysis, on the assumptive existence of heteroclinic orbits, we provide a few of their approximations.
Coupling Systems for a New Type of Phase Synchronization
2016
Using the usual phase in plane, we propose a general method to design coupling between systems that will exhibit phase synchronization. Numerical results are shown for Lorenz systems. Phase synchronization and antiphase synchronization are equally probable depending on initial conditions. A new network with Lorenz phase synchronized system is obtained.
Pattern formation and transition to chaos in a chemotaxis model of acute inflammation
2021
We investigate a reaction-diffusion-chemotaxis system that describes the immune response during an inflammatory attack. The model is a modification of the system proposed in Penner, Ermentrout, and Swigon [SIAM J. Appl. Dyn. Syst., 11 (2012), pp. 629-660]. We introduce a logistic term in the immune cell dynamics to reproduce the macrophages' activation, allowing us to describe the disease evolution from the early stages to the acute phase. We focus on the appearance of pattern solutions and their stability. We discover steady-state (Turing) and wave instabilities and classify the bifurcations deriving the corresponding amplitude equations. We study stationary radially symmetric solutions an…
Hamiltonian tools for the analysis of optical polarization control
2011
Import JabRef; International audience; The study of the polarization dynamics of two counterpropagating beams in optical fibers has recently been the subject of a growing renewed interest, from both the theoretical and experimental points of view. This system exhibits a phenomenon of polarization attraction, which can be used to achieve a complete polarization of an initially unpolarized signal beam, almost without any loss of energy. Along the same way, an arbitrary polarization state of the signal beam can be controlled and converted into any other desired state of polarization, by adjusting the polarization state of the counterpropagating pump beam. These properties have been demonstrate…
Dissipative rogue wave generation in multiple-pulsing mode-locked fiber laser
2013
Following the first experimental observation of a new mechanism leading to optical rogue wave (RW) formation briefly reported in Lecaplain et al (2012 Phys. Rev. Lett. 108 233901), we provide an extensive study of the experimental conditions under which these RWs can be detected. RWs originate from the nonlinear interactions of bunched chaotic pulses that propagate in a fiber laser cavity, and manifest as rare events of high optical intensity. The crucial influence of the electrical detection bandwidth is illustrated. We also clarify the observation of RWs with respect to other pulsating regimes, such as Q-switching instability, that also lead to L-shaped probability distribution functions.…
MR3039719 Reviewed Wang, Lidong; Liu, Heng; Gao, Yuelin Chaos for discrete dynamical system. J. Appl. Math. 2013, Art. ID 212036, 4 pp. (Reviewer: Ga…
2013
In this paper the authors show the relation between the definitions of Li-Yorke chaos and distributional chaos in discrete dynamical systems. In particular, after listing the main definitions and reviewing the known results, the authors prove that: • a discrete dynamical system is chaotic in the sense of Martelli and Wiggins when it exhibits transitive distributional chaos; • a discrete dynamical system is distributively chaotic in a sequence when it is chaotic in the strong sense of Li-Yorke. Finally, the authors prove a sufficient condition for the dynamical system to be chaotic in the strong sense of Li-Yorke.
La morphologie des tissus urbains et périurbains à travers une lecture fractale
2005
Urban expansion produces an irregular urban fabric. This phenomenon influences areas which are distant from urban centres, a problem for sustainable development. Solutions proposed to reduce urban expansion are modelled on the pattern of the compact town. Generally, it is believed that these solutions are unacceptable to the people concerned. In this article we present an alternative approach to the study of urban fabric, which shows that, despite their irregular form, it is possible to describe their development using fractal analysis. This permits understanding of the socio-economic causes of this process and the development an alternative conceptual approach to the management of urban ex…
Has palaeontology answers for some current environmental problems?
2021
History as an irreversible process has no role from a uniformitarian point of view in geology and palaeobiology. Contingency is another trait of history and particle palaeontology has its foundation on such principles. However, new approaches in physics and the theory of systems point out the need to consider a time arrow. Moreover, chance and necessity are interwoven in synergetics and self-organization theory and there may be some possibility of prediction. The global biota has a history resulting from a process of self-organization. A rich fossil record was produced during the Phanerozoic times and this fossil record shows us how life overcame several important crisis. A clear understand…