Statistics of Lyapunov exponent spectrum in randomly coupled Kuramoto oscillators

Patra, Soumen K.; Ghosh, Anandamohan

doi:10.1103/physreve.93.032208

Cited by 14 publications

(18 citation statements)

References 30 publications

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“…The Lyapunov exponent distribution in the above mentioned supersymmetric model, used by the string theory community, was shown to follow the semi-circle law. Furthermore, in the Kuramoto model of N oscillators with variable coupling matrix similar findings have been reported, where the presence of Poisson or Wigner surmise distribution in the Lyapunov exponent spacings is taken as an indicator for synchronization behavior [13]. Historically, authors in [14] were the first to show the existence of neighboring Lyapunov exponents repulsion, hinting at the similarities in behavior of Lyapunov exponents and the Gaussian RMT ensembles.…”

Section: Introductionsupporting

confidence: 61%

Random Matrix Ensembles in Hyperchaotic Classical Dissipative Dynamical Systems

Odavić¹,

Mali²

2019

Preprint

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We study the statistical fluctuations of Lyapunov exponents in the discrete version of the nonintegrable perturbed sine-Gordon equation, the dissipative ac+dc driven Frenkel-Kontorova model. Our analysis shows that the fluctuations of the exponent spacings in the strictly overdamped limit, which is nonchaotic, conforms to the uncorrelated Poisson distribution. By studying the spatiotemporal dynamics we relate the emergence of the Poissonian statistics to the Middleton's no-passing rule. Next, by scanning over the dc driving and particle mass we identify several parameter regions for which this one-dimensional model exhibits hyperchaotic behavior. Furthermore, in the hyperchaotic regime where roughly fifty percent of exponents is positive, the fluctuations exhibit features of the correlated universal statistics of the Gaussian Orthogonal Ensemble (GOE). Due to the dissipative nature of the dynamics we find that the match, between the Lyapunov spectrum statistics and the universal statistics of GOE, is not complete. Finally, we present evidence supporting the existence of the Tracy-Widom distribution in the fluctuation statistics of the largest Lyapunov exponent.

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Section: Introductionsupporting

confidence: 61%

Random Matrix Ensembles in Hyperchaotic Classical Dissipative Dynamical Systems

Odavić¹,

Mali²

2019

Preprint

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“…The computation time is essentially the convergence rate of a coupled oscillator network. Existing study on this subject is rather scattered [34][35][36][37][38]. Exact analytical solutions of the convergence rate of the Kuramoto model are difficult to acquire [34].…”

Section: Speed and Scalabilitymentioning

confidence: 99%

“…Exact analytical solutions of the convergence rate of the Kuramoto model are difficult to acquire [34]. In some studies, the spectrum of Lyapunov exponents of the locked states in the Kuramoto model are used to analyze its speed and calculated for specific problems [37,38]; how it scales with the problem size is yet to be studied. Therefore, in this section, we analyze the convergence speed of coupled oscillators through a computational study.…”

Section: Speed and Scalabilitymentioning

confidence: 99%

Oscillator-based Ising Machine

Wang,

Roychowdhury

2017

Preprint

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Many combinatorial optimization problems can be mapped to finding the ground states of the corresponding Ising Hamiltonians. The physical systems that can solve optimization problems in this way, namely Ising machines, have been attracting more and more attention recently. Our work shows that Ising machines can be realized using almost any nonlinear self-sustaining oscillators with logic values encoded in their phases. Many types of such oscillators are readily available for large-scale integration, with potentials in high-speed and low-power operation. In this paper, we describe the operation and mechanism of oscillator-based Ising machines. The feasibility of our scheme is demonstrated through several examples in simulation and hardware, among which a simulation study reports average solutions exceeding those from state-of-art Ising machines on a benchmark combinatorial optimization problem of size 2000.

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“…Lemma 3: [34] For matrices P, Q, R and S , symmetric matrix Z > 0 and constant > 0 satisfying RR T < I and −1 I − S ZS T > 0, the inequality…”

Section: Resultsmentioning

confidence: 99%

Recursive Minimum-Variance Filter Design for State-Saturated Complex Networks With Uncertain Coupling Strengths Subject to Deception Attacks

Gao

Dong

Wang

et al. 2022

IEEE Trans. Cybern.

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In this paper, the recursive filtering problem is investigated for state-saturated complex networks (CNs) subject to uncertain coupling strengths (UCSs) and deception attacks. The measurement signals transmitted via the communication network may suffer from deception attacks which are governed by Bernoulli-distributed random variables. The purpose of the problem under consideration is to design a minimum-variance filter for CNs with deception attacks, state saturations and UCSs such that upper bounds on the resulting error covariances are guaranteed. Then, the expected filter gains are acquired via minimizing the traces of such upper bounds and sufficient conditions are established to ensure the exponential mean-square boundedness of the filtering errors. At last, two simulation examples (including a practical application) are exploited to validate the effectiveness of our designed approach.

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Statistics of Lyapunov exponent spectrum in randomly coupled Kuramoto oscillators

Cited by 14 publications

References 30 publications

Random Matrix Ensembles in Hyperchaotic Classical Dissipative Dynamical Systems

Random Matrix Ensembles in Hyperchaotic Classical Dissipative Dynamical Systems

Oscillator-based Ising Machine

Recursive Minimum-Variance Filter Design for State-Saturated Complex Networks With Uncertain Coupling Strengths Subject to Deception Attacks

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