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The dynamical symmetry breaking in a two-field model is studied by numerically solving the coupled effective field equations. These are dissipative equations of motion that can exhibit strong chaotic dynamics. By choosing very general model…

High Energy Physics - Theory · Physics 2009-10-31 Rudnei O. Ramos , F. A. R. Navarro

Certain deterministic non-linear systems may show chaotic behaviour. Time series derived from such systems seem stochastic when analyzed with linear techniques. However, uncovering the deterministic structure is important because it allows…

chao-dyn · Physics 2008-02-03 Dimitris Kugiumtzis , Bjoern Lillekjendlie , Nils Christophersen

We show how a recently introduced statistics [Patil et al, Phys. Rev. Lett. 81 5878 (2001)] provides a direct relationship between dimension and predictability in spatiotemporal chaotic systems. Regions of low dimension are identified as…

Chaotic Dynamics · Physics 2007-05-23 Gerson Francisco , Paulsamy Muruganandam

Chaos reveals a fundamental paradox in the scientific understanding of Complex Systems. Although chaotic models may be mathematically deterministic, they are practically non-determinable due to the finite precision, which is inherent in all…

We study simple models of intermittency, involving switching between two states, within the dynamical large-deviation formalism. Singularities appear in the formalism when switching is cooperative, or when its basic timescale diverges. In…

Statistical Mechanics · Physics 2018-06-13 Stephen Whitelam

We propose a computational method for large deviation statistics of time-averaged quantities in general Markov processes. In our proposed method, we repeat a response measurement against external forces, where the forces are determined by…

Statistical Mechanics · Physics 2014-03-12 Takahiro Nemoto , Shin-ichi Sasa

The phase ordering dynamics of coupled chaotic maps on fractal networks are investigated. The statistical properties of the systems are characterized by means of the persistence probability of equivalent spin variables that define the…

Chaotic Dynamics · Physics 2007-05-23 K. Tucci , M. G. Cosenza , O. Alvarez-Llamoza

We train an artificial neural network which distinguishes chaotic and regular dynamics of the two-dimensional Chirikov standard map. We use finite length trajectories and compare the performance with traditional numerical methods which need…

Machine Learning · Computer Science 2020-04-24 Woo Seok Lee , Sergej Flach

We present an efficient approach, based on a number-conditioned master equation, for large-deviation analysis in mesoscopic transports. Beyond the conventional full-counting-statistics study, the large-deviation approach encodes complete…

Mesoscale and Nanoscale Physics · Physics 2011-09-30 Jun Li , Yu Liu , Jing Ping , Shu-Shen Li , Xin-Qi Li , YiJing Yan

For a system of globally coupled chaotic maps with bistable behaviour we relate the rate function for large deviations in the system size at finite time to dynamical properties of the self consistent Perron-Frobenius operator (SCPFO) that…

Dynamical Systems · Mathematics 2010-09-09 Gerhard Keller

To make predictions or design control, information on local sensitivity of initial conditions and state-space contraction is both central, and often instrumental. However, it is not always simple to reliably determine instability fields or…

Grebogi, Ott and Yorke (Phys. Rev. A 38(7), 1988) have investigated the effect of finite precision on average period length of chaotic maps. They showed that the average length of periodic orbits ($T$) of a dynamical system scales as a…

Chaotic Dynamics · Physics 2009-11-13 Nithin Nagaraj , Mahesh C. Shastry , Prabhakar G. Vaidya

Most of the time series in nature are a mixture of signals with deterministic and random dynamics. Thus the distinction between these two characteristics becomes important. Distinguishing between chaotic and aleatory signals is difficult…

Data Analysis, Statistics and Probability · Physics 2017-09-13 D. M. Mateos , L. Riveaud , P. W. Lamberti

We study the transition to synchronization in large, dense networks of chaotic circle maps, where an exact solution of the mean-field dynamics in the infinite network and all-to-all coupling limit is known. In dense networks of finite size…

Disordered Systems and Neural Networks · Physics 2023-07-06 Hans Muller Mendonca , Ralf Tönjes , Tiago Pereira

Chaotic systems have been investigated in several areas of engineering. In control theory, such systems have instigated the emergence of new techniques as well, have been used as a source of noise generation. The application of chaotic…

Signal Processing · Electrical Eng. & Systems 2019-10-15 M. Teixeira , N. P. Basilio , D. L. Firmo , E. G. Nepomuceno , J. Arias-Garcia

The scaling behavior of the maximal Lyapunov exponent in chaotic systems with time-delayed feedback is investigated. For large delay times it has been shown that the delay-dependence of the exponent allows a distinction between strong and…

Chaotic Dynamics · Physics 2012-10-15 Thomas Jüngling , Wolfgang Kinzel

We investigate the dynamics of an array of logistic maps coupled with random delay times. We report that for adequate coupling strength the array is able to synchronize, in spite of the random delays. Specifically, we find that the…

Chaotic Dynamics · Physics 2009-11-10 Cristina Masoller , Arturo C. Marti

By an inductive reasoning, and based on recent results of the joint moments of proper delay times of open chaotic systems for ideal coupling to leads, we obtain a general expression for the distribution of the partial delay times for an…

Mesoscale and Nanoscale Physics · Physics 2017-11-28 A. M. Martínez-Argüello , A. A. Fernández-Marín , M. Martínez-Mares

Designing chaotic maps with complex dynamics is a challenging topic. This paper introduces the nonlinear chaotic processing (NCP) model, which contains six basic nonlinear operations. Each operation is a general framework that can use…

Chaotic Dynamics · Physics 2016-12-16 Zhongyun Hua , Yicong Zhou

In the last decade it has been shown that a large class of phase oscillator models admit low dimensional descriptions for the macroscopic system dynamics in the limit of an infinite number N of oscillators. The question of whether the…

Chaotic Dynamics · Physics 2017-09-13 Per Sebastian Skardal , Juan G. Restrepo , Edward Ott