Complexity and synchronization in stochastic chaotic systems

Dang, Thai Son; Palit, Sanjay Kumar; Mukherjee, Sayan; Hoang, Thang Manh; Banerjee, Santo

doi:10.1140/epjst/e2016-02616-9

Cited by 21 publications

(11 citation statements)

References 28 publications

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“…Complexity measures are of trending interest in both classical and quantum systems. It is very effective to quantify the 'uncertain' phenomenon in several branches of Science, Engineering and Management [34][35][36][37][38][39]. For example, the structure of an organization is complex, may not be chaotic.…”

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confidence: 99%

Complexity, Chaos and Fluctuations

Banerjee

Colangeli

2017

Eur. Phys. J. Spec. Top.

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This EPJ special topics issue is a collection of contributions about some recent developments in statistical mechanics and dynamical complexity. The various articles report results on statistical fluctuations, non equilibrium models, chaos and nonlinear interactions, complexity and its various associated measures.The long-standing endeavor of Statistical Mechanics is to establish a mathematical framework which allows to encompass different levels of description of a many-particle system: (i) the microscopic setting, stemming from the Boltzmann-Gibbs statistical ensemble theory [1, 2]; (ii) the mesoscopic scale, typically described in the framework of kinetic theory [3-5], interacting particle systems [6][7][8][9][10][11][12] or even more general stochastic processes [13,14]; (iii) the macroscopic level, which is the standard set-up in contexts such as the derivation of hydrodynamic equations, turbulence [15][16][17], Irreversible Thermodynamics [18], etc. Equilibrium phenomena have been investigated and understood much more thoroughly than non-equilibrium ones. At present, the equilibrium theory may be considered complete, for what concerns the microscopic foundations of equilibrium thermodynamics, including the theory of phase transitions and critical phenomena. On the other hand, in spite of the long-standing research activity, Nonequilibrium Statistical Mechanics is still an open field of research. One of the reasons is that nonequilibrium phenomena are so numerous, diverse and complex that attaining a unified description may still appear as an elusive ambition. In particular, away from equilibrium one cannot bypass the analysis of the microscopic dynamics even in the study of stationary states, that are the simplest beyond equilibrium.Nevertheless, relevant progresses were made in this field in the last decades, cf.[19]. We refer, for instance, to the discovery of the Fluctuation Relations for deterministic and stochastic dynamics [20][21][22]. Much effort was needed, in particular, to identify the minimal mathematical ingredients as well as the physical mechanisms lying beneath the validity of such relations [23][24][25]. Another result, whose mathematical theory was originally dug out in the sixties of the last century [26,27] and was then gradually a

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confidence: 99%

Complexity, Chaos and Fluctuations

Banerjee

Colangeli

2017

Eur. Phys. J. Spec. Top.

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“…Complexity of nonlinear dynamical systems has attracted attention in recent years due to its importance for measuring the predictability and randomness of the system time series [31,32]. The time series with high complexity led to a chaotic attractor, hence, the complexity is able to determine and locate the chaotic and periodic attractors in nonlinear systems [33,34].…”

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confidence: 99%

Dynamics and Complexity of a New 4D Chaotic Laser System

Natiq

Said

Al-Saidi

et al. 2019

Entropy

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Derived from Lorenz-Haken equations, this paper presents a new 4D chaotic laser system with three equilibria and only two quadratic nonlinearities. Dynamics analysis, including stability of symmetric equilibria and the existence of coexisting multiple Hopf bifurcations on these equilibria, are investigated, and the complex coexisting behaviors of two and three attractors of stable point and chaotic are numerically revealed. Moreover, a conducted research on the complexity of the laser system reveals that the complexity of the system time series can locate and determine the parameters and initial values that show coexisting attractors. To investigate how much a chaotic system with multistability behavior is suitable for cryptographic applications, we generate a pseudo-random number generator (PRNG) based on the complexity results of the laser system. The randomness test results show that the generated PRNG from the multistability regions fail to pass most of the statistical tests.

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“…The articles can be grouped into four categories, namely 1. Synchronization and control in time delayed and other networks [23][24][25][26][27][28][29] [36][37][38][39][40][41].…”

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confidence: 99%

“…The last section contains dynamical properties, synchronization and control in various stochastic and deterministic models [36][37][38][39][40][41]. In [36] the dynamical regimes has been investigated, which may be observed in an ensemble of inhibitory coupled Rulkov elements depending on coupling values.…”

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Synchronization and control in time-delayed complex networks and spatio-temporal patterns

Banerjee

Kurths

Schöll

2016

Eur. Phys. J. Spec. Top.

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Abstract. This special topics issue is a collection of contributions on the recent developments of control and synchronization in time delayed systems and space time chaos. The various articles report interesting results on time delayed complex networks; fractional order delayed models; dynamics of spatio-temporal patterns; stochastic models etc. Experimental analysis on synchronization, dynamics and control of chaos are also well investigated using Field Programmable Gate Array (FPGA), circuit realizations and chemical reactions.Complexity and networks, originated in different contexts have been received much attention as interdisciplinary subjects. Of late, they are found to be jointly associated to characterize the so-called complex networked model in different areas that range from natural phenomena on technological aspects to socio-economic systems. It has been reported well that complex networks (CN) widely exist in the real world, including food webs, communication networks, social networks, power grids, cellular and metabolic networks, world wide web, disease transmission networks,neural networks, electrical power grids, scientific citation web, living organisms, etc. [1,2].Complex networks are involved in a number of different fields that include physics, chemistry, computer science, sociology, economics, finance, biology, epidemiology, etc. However in all of these CN's a very common feature is the presence of a large number of objects (e.g. individuals, computers, cells, molecules, etc.), which interact in a way that quantifies strong irregularities. A network can be essentially represented by a graph, an abstract mathematical structure consists of a set of generically called nodes (vertices) connected by links (edges) representing some binary relationship. In case of World Wide Web, the websites are the nodes and the hyperlinks between a

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Complexity and synchronization in stochastic chaotic systems

Cited by 21 publications

References 28 publications

Complexity, Chaos and Fluctuations

Complexity, Chaos and Fluctuations

Dynamics and Complexity of a New 4D Chaotic Laser System

Synchronization and control in time-delayed complex networks and spatio-temporal patterns

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