245 research outputs found
A Chaotic System with an Infinite Number of Equilibrium Points: Dynamics, Horseshoe, and Synchronization
Discovering systems with hidden attractors is a challenging topic which has received considerable interest of the scientific community recently. This work introduces a new chaotic system having hidden chaotic attractors with an infinite number of equilibrium points. We have studied dynamical properties of such special system via equilibrium analysis, bifurcation diagram, and maximal Lyapunov exponents. In order to confirm the systemâs chaotic behavior, the findings of topological horseshoes for the system are presented. In addition, the possibility of synchronization of two new chaotic systems with infinite equilibria is investigated by using adaptive control
Decidability and Universality in Symbolic Dynamical Systems
Many different definitions of computational universality for various types of
dynamical systems have flourished since Turing's work. We propose a general
definition of universality that applies to arbitrary discrete time symbolic
dynamical systems. Universality of a system is defined as undecidability of a
model-checking problem. For Turing machines, counter machines and tag systems,
our definition coincides with the classical one. It yields, however, a new
definition for cellular automata and subshifts. Our definition is robust with
respect to initial condition, which is a desirable feature for physical
realizability.
We derive necessary conditions for undecidability and universality. For
instance, a universal system must have a sensitive point and a proper
subsystem. We conjecture that universal systems have infinite number of
subsystems. We also discuss the thesis according to which computation should
occur at the `edge of chaos' and we exhibit a universal chaotic system.Comment: 23 pages; a shorter version is submitted to conference MCU 2004 v2:
minor orthographic changes v3: section 5.2 (collatz functions) mathematically
improved v4: orthographic corrections, one reference added v5:27 pages.
Important modifications. The formalism is strengthened: temporal logic
replaced by finite automata. New results. Submitte
A New Chaotic System with Line of Equilibria: Dynamics, Passive Control and Circuit Design
A new chaotic system with line equilibrium is introduced in this paper. This system consists of five terms with two transcendental nonlinearities and two quadratic nonlinearities. Various tools of dynamical system such as phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, bifurcation diagram and PoincarÚ map are used. It is interesting that this system has a line of fixed points and can display chaotic attractors. Next, this paper discusses control using passive control method. One example is given to insure the theoretical analysis. Finally, for the new chaotic system, An electronic circuit for realizing the chaotic system has been implemented. The numerical simulation by using MATLAB 2010 and implementation of circuit simulations by using MultiSIM 10.0 have been performed in this study
Readings in the 'New Science': a selective annotated bilbiography
Die vorliegende kommentierte Bibliographie will hauptsĂ€chlich Historikern eine Orientierungshilfe fĂŒr die LiteraturfĂŒlle zum Thema 'New Science' geben. Die knapp besprochenen Arbeiten sind nach folgenden Themenkomplexen gruppiert: Unentscheidbarkeit, UngewiĂheit und KomplexitĂ€t; Makrostrukturen: Systeme und die humane Dimension; Dynamische Systeme (Spieltheorie, Katastrophentheorie, Chaos, Fraktale Geometrie, Antizipatorische Systeme, Lebende Systeme); Computer (Informationstheorie, Kognitionswisssenschaft und KĂŒnstliche Intelligenz); Die Mikro- und die Makrodimensionen; Zeit; Kultur und Erkenntnistheorie. (pmb
Complexity, Emergent Systems and Complex Biological Systems:\ud Complex Systems Theory and Biodynamics. [Edited book by I.C. Baianu, with listed contributors (2011)]
An overview is presented of System dynamics, the study of the behaviour of complex systems, Dynamical system in mathematics Dynamic programming in computer science and control theory, Complex systems biology, Neurodynamics and Psychodynamics.\u
Dynamics of excitable cells: spike-adding phenomena in action
We study the dynamics of action potentials of some electrically excitable cells: neurons and cardiac muscle cells. Bursting, following a fastâslow dynamics, is the most characteristic behavior of these dynamical systems, and the number of spikes may change due to spike-adding phenomenon. Using analytical and numerical methods we give, by focusing on the paradigmatic 3D HindmarshâRose neuron model, a review of recent results on the global organization of the parameter space of neuron models with bursting regions occurring between saddle-node and homoclinic bifurcations (fold/hom bursting). We provide a generic overview of the different bursting regimes that appear in the parametric phase space of the model and the bifurcations among them. These techniques are applied in two realistic frameworks: insect movement gait changes and the appearance of Early Afterdepolarizations in cardiac dynamics
Particles Of Light, Webs Of Interaction: [Dr. Floyd Ratliff]
Rockefeller University Research Profiles are a series of scientific profiles that were published quarterly, from 1980-1990, by the Rockefeller University. Each issue features the research and achievements of an individual Rockefeller University scientist.https://digitalcommons.rockefeller.edu/research_profiles/1007/thumbnail.jp
- âŠ