Search

The reservoir computing (RC) is increasingly used to learn the synchronization behavior of chaotic systems as well as the dynamical behavior of complex systems, but it is scarcely applied in studying synchronization of non-smooth chaotic systems likely due to its complexity leading to the unimpressive effect. Here proposes a simulated annealing-based differential evolution (SADE) algorithm for the optimal parameter selection in the reservoir, and constructs an improved RC model for synchronization, which can work well not only for non-smooth chaotic systems but for smooth ones. Extensive simulations show that the trained RC model with optimal parameters has far longer prediction time than those with empirical and random parameters. More importantly, the well-trained RC system can be well synchronized to its original chaotic system as well as its replicate RC system via one shared signal, whereas the traditional RC system with empirical or random parameters fails for some chaotic systems, particularly for some non-smooth chaotic systems. [ABSTRACT FROM AUTHOR]

In 2014, Khalil et al. [2014] proposed the conformable fractional derivative, which obeys chain rule and the Leibniz rule. In this paper, motivated by the monograph of Jibin Li [Li, 2013], we study the exact traveling wave solutions for a class of third-order MKdV equations with the conformable fractional derivative. Our approach is based on the bifurcation theory of planar dynamical systems, which is much different from the simplest equation method proposed in [Chen & Jiang, 2018]. By employing the traveling wave transformation u (x , t) = ϕ (ξ) , ξ = k x + v t α , we reduce the PDE to an ODE which depends on the fractional order α , then the analysis depends on the order α. Moreover, as α = 1 , the exact solutions are consistent with the integer PDE. However, in all the existing papers, the reduced ODE is independent of the fractional order α. It is believed that this method can be applicable to solve the other nonlinear differential equations with the conformable fractional derivative. [ABSTRACT FROM AUTHOR]

In this paper, we prove the reducibility of a class of nonlinear periodic differential equation with degenerate equilibrium point under small perturbations, and obtain a periodic solution near the equilibrium point. The result is new and more general, including that of the paper [X. Lu and J. Xu, On small perturbations of a nonlinear periodic system with degenerate equilibrium, Nonlinear Differ. Equ. Appl. 21 (2014), pp. 361-370 ]. [ABSTRACT FROM AUTHOR]

This paper presents two numerical schemes for solving the Allen–Cahn equation representing a model for antiphase domain coarsening in a binary mixture. Based on the operator splitting method, the Allen–Cahn equation was divided into a linear and a nonlinear sub equation: the linear sub equation was solved by a Fourier spectral method, which is based on the exact solution and thus has no stability restriction on the time-step size; the nonlinear sub equation was then solved analytically due to the availability of a closed-form solution. The stability and error analysis of the numerical solution are presented in detail. Numerical experiments are presented to confirm the accuracy, efficiency, and stability of the proposed method. In particular, we show that the schemes are unconditionally stable and second-order accurate in time. [ABSTRACT FROM PUBLISHER]

According to the master stability function (MSF) framework, synchronized regions play an extremely important role in network synchronization. On these grounds, this paper casts sight on network synchronous state stability via studying the bifurcation (or transition) problem of network synchronized regions with varying nodal dynamics, and the effects of time delay on the bifurcation of synchronized regions. Theoretical and numerical investigations show that in complex networks with coupling delay, there exist rich bifurcation behaviors of synchronized regions. The coupling delay can not only enlarge or narrow synchronized regions, but also change bifurcation points. More importantly, a very small delay can result in the conversion of an unbounded or empty synchronized region into a bounded one, implying that coupling delay can enhance or suppress synchronization in complex dynamical networks. These results will further strengthen our understanding for synchronous state stability in complex dynamical networks. [ABSTRACT FROM AUTHOR]

In this paper, we apply IAAFT to generate surrogate time series of measured multivariate time series. A quantitative method to detect nonlinearity in multivariate time series is proposed using the generalized redundancy and linear redundancy as the significance test statistic. The null hypothesis of a multivariate linear Gaussian random process is tested using the multivariate surrogate data. The validity of this method is demonstrated using two types models (linear and nonlinear) and applied to Shanghai stock market. [ABSTRACT FROM AUTHOR]

Based on the fact that most of real networks are directed and weighted, and the breeding of new connections generally affects the communication capacity of neighbor nodes, this paper proposes a strength-based instead of degree-based directed weighted scale-free network model where an adaptive weight evolution mechanism is introduced, and the newly added edges between existing nodes besides between existing nodes and the new node are involved in. Theoretical analysis shows the strength (in-strength and out-strength) distribution as well as degree (in-degree and out-degree) distribution of networks generated by our presented model follow a power law distribution, indicating the network is with scale-free characteristic, and the power-law exponent is independent of network size, but depends on the basic edge weight, the weight increment and the number of newly added edges. Numerous simulations further verify that numerical results are well consistent with the theoretical results, and the dependence of power-law exponents on the aforementioned parameters are also analyzed and discussed. In addition, the topological characteristics of the directed weighted scale-free network, such as the average clustering coefficient and the average path length, are demonstrated as well. • The model aims at the directed and weighted network, and it is based on node's strength distribution. • An adaptive evolution mechanism is introduced in generating networks. • The new edges are bred not only between the new node and existing nodes, but between existing nodes. • The model is verified by theoretical analysis and numerical simulations. • The impact of initial setting parameters on the scale-free characteristic is discussed. [ABSTRACT FROM AUTHOR]

This paper is concerned with the synchronization of stochastic delayed multilayer networks with additive couplings. Multilayer networks are a kind of complex networks with different layers, which consist of different kinds of interactions or multiple subnetworks. Additive couplings are designed to capture the different layered connections. Based on additive couplings, several sufficient conditions are obtained to guarantee the synchronization of chaotic stochastic delayed coupled multilayer network. More specifically, on one hand, we obtain some sufficient conditions to guarantee that the stochastic multilayer network can be synchronized almost surely without control input. On the other hand, we propose three synchronization schemes by designing controllers. Scheme I: It is assumed that only a part of the nodes are allowed to be controlled directly. Scheme II: Control all nodes of the complex system by using only one controller. Scheme III: Pinning adaptive controller. Finally, an example and its simulations are given to show the effectiveness of our control schemes. [ABSTRACT FROM AUTHOR]

In this article, generalized pinning synchronization problem is investigated for a class of Cohen–Grossberg neural networks with discontinuous neuron activations and mixed delays. By designing generalized pinning state-feedback and adaptive controllers, several criteria for global exponential synchronization and global asymptotical synchronization of the drive–response based system are obtained in view of non-smooth analysis theory with generalized Lyapunov functional method, in which first pinning the neurons with very small self-inhibition and small amplification functions is pointed out. Some numerical examples are given to illustrate the feasibility of the obtained results. [ABSTRACT FROM AUTHOR]

This paper investigates the impact of edge-adding number m and edge-adding distance d on both synchronizability and average path length of NW small-world networks generated from ring networks via random edge-adding. It is found that the synchronizability of the network as a function of the distance d is fluctuant and there exist some d that have almost no impact on the synchronizability and may only scarcely shorten the average path length of the network. Numerical simulations on a network of Lorenz oscillators confirm the above results. This phenomenon shows that the contributions of randomly added edges to both the synchronizability and the average path length are not uniform nor monotone in building an NW small-world network with equal-distance edge additions, implying that only if appropriately adding edges when building up the NW small-word network can help enhance the synchronizability and/or reduce the average path length of the resultant network. Finally, it is shown that this NW small-world network has worse synchronizability and longer average path length, when compared with the conventional NW small-world network, with random-distance edge additions. This may be due to the fact that with equal-distance edge additions, there is only one shortcut distance for better information exchange among nodes and for shortening the average path length, while with random-distance edge additions, there exist many different distances for doing so. [ABSTRACT FROM AUTHOR]

We consider a variant of the mean-field model of coupled phase oscillators with uniform distribution of natural frequencies. By establishing correlations between the quenched disorder of intrinsic frequencies and coupling strength with both in- and out-coupling heterogeneities, we reveal a generic criterion for the onset of partial locking that takes place in a domain with the coexistence of phase-locked oscillators and drifters. The critical points manifesting the instability of the stationary states are obtained analytically. In particular, the bifurcation mechanism of the equilibrium states is uncovered by the use of frequency-dependent version of the Ott–Antonsen reduction consistently with the analysis based on the self-consistent approach. We demonstrate that both the manner of coupling heterogeneity and correlation exponent have influence on the emergent patterns of partial locking. Our research could find applicability in better understanding the phase transitions and related collective phenomena involving synchronization control in networked systems. [ABSTRACT FROM AUTHOR]