790 research outputs found
Existence of random attractors for a class of second order lattice dynamical systems with Brownian motions
Copyright © 2014 Yamin Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.For abstract, see attached file.The National Natural Science Foundation of China under Grant nos. 61374010, 61074129, and 61175111, the Natural Science Foundation of Jiangsu Province of China under Grant BK2012682, the Qing
Lan Project of Jiangsu Province (2010), the 333 Project of Jiangsu Province (2011), and the Six Talents Peak Project of Jiangsu Province (DZXX-047)
Mutual synchronization and clustering in randomly coupled chaotic dynamical networks
We introduce and study systems of randomly coupled maps (RCM) where the
relevant parameter is the degree of connectivity in the system. Global
(almost-) synchronized states are found (equivalent to the synchronization
observed in globally coupled maps) until a certain critical threshold for the
connectivity is reached. We further show that not only the average
connectivity, but also the architecture of the couplings is responsible for the
cluster structure observed. We analyse the different phases of the system and
use various correlation measures in order to detect ordered non-synchronized
states. Finally, it is shown that the system displays a dynamical hierarchical
clustering which allows the definition of emerging graphs.Comment: 13 pages, to appear in Phys. Rev.
Synchronization of non-chaotic dynamical systems
A synchronization mechanism driven by annealed noise is studied for two
replicas of a coupled-map lattice which exhibits stable chaos (SC), i.e.
irregular behavior despite a negative Lyapunov spectrum. We show that the
observed synchronization transition, on changing the strength of the stochastic
coupling between replicas, belongs to the directed percolation universality
class. This result is consistent with the behavior of chaotic deterministic
cellular automata (DCA), supporting the equivalence Ansatz between SC models
and DCA. The coupling threshold above which the two system replicas synchronize
is strictly related to the propagation velocity of perturbations in the system.Comment: 16 pages + 12 figures, new and extended versio
Timing of Transients : Quantifying Reaching Times and Transient Behavior in Complex Systems
The authors thank the anonymous referees for their detailed and constructive feedback. This paper was developed within the scope of the IRTG 1740/TRP 2011/50151-0, funded by the DFG/FAPESP. This work was conducted in the framework of PIK’s flagship project on coevolutionary pathways (copan). The authors thank CoNDyNet (FKZ 03SF0472A) for their cooperation. The authors gratefully acknowledge the European Regional Development Fund (ERDF), the German Federal Ministry of Education and Research and the Land Brandenburg for supporting this project by providing resources on the high performance computer system at the Potsdam Institute for Climate Impact Research. The authors thank the developers of the used software: Python[47], Numerical Python[48] and Scientific Python[49]. The authors thank Sabine Auer, Karsten Bolts, Catrin Ciemer, Jonathan Donges, Reik Donner, Jasper Franke, Frank Hellmann, Jakob Kolb, Chiranjit Mitra, Finn Muller-Hansen, Jan Nitzbon, Anton Plietzsch Stefan Ruschel, Tiago Pereira da Silva, Francisco A. Rodrigues, Paul Schultz, and Lyubov Tupikina for helpful discussions and comments.Peer reviewedPublisher PD
A Note On Asymptotic Smoothness Of The Extensions Of Zadeh
The concept of asymptotic smooth transformation was introduced by J. Hale [10]. It is a very important property for a transformation between complete metric spaces to have a global attractor. This property has also consequences on asymptotic stability of attractors. In our work we study the conditions under which the Zadeh's extension of a continuous map f : R n → R n is asymptotically smooth in the complete metric space JF(R n) of normal fuzzy sets with the induced Hausdorff metric d ∞ (see Kloeden and Diamond [8]).212141153Barros, L.C., Bassanezi, R.C., Tonelli, P.A., On the continuity of Zadeh's extension (1997) Proceedings Seventh IFSA World Congress, 2, pp. 3-8. , PragueBarros, L.C., Bassanezi, R.C., Tonelli, P.A., Fuzzy modeling in populations dynamics (2000) Ecological Modeling, 128, pp. 27-33Brumley, W.E., On the asymptotic behavior of solutions of differential difference equations of neutral type (1970) J. of Differential Equations, 7, pp. 175-188Cabrelli, C.A., Forte, B., Molter, U., Vrscay, E., Iterated Fuzzy Sets Systems: A new approach to the inverse for fractals and other sets (1992) J. of Math. Anal, and Appl., 171, pp. 79-100Cooperman, G., (1978) α-Condensing Maps and Dissipative Processes, , Ph. D. Thesis, Brown University, Providence, R. IDiamond, P., Chaos in iterated fuzzy systems (1994) J. of Mathematical Analysis and Applications, 184, pp. 472-484Diamond, P., Time Dependent Differential Inclusions, Cocycle Attractors and Fuzzy Differential Equations (1999) IEEE Trans. on Fuzzy Systems, 7, pp. 734-740Diamond, P., Kloeden, P., (1994) Metric Spaces of Fuzzy Sets: Theory and Applications, , World Scientific PubFriedmann, M., Ma, M., Kandel, A., Numerical solutions of fuzzy differential and integral equations (1999) Fuzzy Sets and Systems, 106, pp. 35-48Hale, J.K., Asymptotic Behavior of Dissipative Systems (1988) Math. Surveys and Monographs, 25. , American Mathematical Society, ProvidenceHüllermeier, E., An Approach to Modeling and Simulation of Uncertain Dynamical Systems (1997) J. Uncertainty, Fuzziness, Know Ledge-Bases Syst., 5, pp. 117-137Kloeden, P.E., Fuzzy dynamical systems (1982) Fuzzy Sets and Systems, 7, pp. 275-296Kloeden, P.E., Chaotic iterations of fuzzy sets (1991) Fuzzy Sets and Systems, 42, pp. 37-42Nguyen, H.T., A note on thé extension principle for fuzzy sets (1978) J. Math. Anal. Appl., 64, pp. 369-380Puri, M.L., Ralescu, D.A., Fuzzy Random Variables (1986) J. of Mathematical Analysis and Applications, 114, pp. 409-422Roman-Flores, H., Barros, L.C., Bassanezzi, R., A note on Zadeh's Extensions (2001) Fuzzy Sets and Systems, 117, pp. 327-331Roman-Flores, H., On the Compactness of E(X) (1998) Appl. Math. Lett., 11, pp. 13-17Zadeh, L.A., Fuzzy sets (1965) Inform. Control, 8, pp. 338-35
Network synchronization of groups
In this paper we study synchronized motions in complex networks in which
there are distinct groups of nodes where the dynamical systems on each node
within a group are the same but are different for nodes in different groups.
Both continuous time and discrete time systems are considered. We initially
focus on the case where two groups are present and the network has bipartite
topology (i.e., links exist between nodes in different groups but not between
nodes in the same group). We also show that group synchronous motions are
compatible with more general network topologies, where there are also
connections within the groups
Review on computational methods for Lyapunov functions
Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both in theory and applications. They provide sufficient conditions for the stability of equilibria or more general invariant sets, as well as for their basin of attraction. The necessity, i.e. the existence of Lyapunov functions, has been studied in converse theorems, however, they do not provide a general method to compute them. Because of their importance in stability analysis, numerous computational construction methods have been developed within the Engineering, Informatics, and Mathematics community. They cover different types of systems such as ordinary differential equations, switched systems, non-smooth systems, discrete-time systems etc., and employ di_erent methods such as series expansion, linear programming, linear matrix inequalities, collocation methods, algebraic methods, set-theoretic methods, and many others. This review brings these different methods together. First, the different types of systems, where Lyapunov functions are used, are briefly discussed. In the main part, the computational methods are presented, ordered by the type of method used to construct a Lyapunov function
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