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Fei Su, Jiang Wang, Huiyan Li, Bin Deng, Haitao Yu, Chen Liu
Controllability and observability analyses are important prerequisite for designing suitable neural control strategy, which can help lower the efforts required to control and observe the system dynamics. First, 3-neuron motifs including the excitatory motif, the inhibitory motif, and the mixed motif are constructed to investigate the effects of single neuron and synaptic dynamics on network controllability (observability). Simulation results demonstrate that for networks with the same topological structure, the controllability (observability) of the node always changes if the properties of neurons and synaptic coupling strengths vary...
February 2017: Chaos
Wen Jiang, Boya Wei, Yongchuan Tang, Deyun Zhou
Complex networks are widely used in modeling complex system. How to aggregate data in complex systems is still an open issue. In this paper, an ordered visibility graph average aggregation operator is proposed which is inspired by the complex network theory and Newton's law of universal gravitation. First of all, the argument values are ordered in descending order. Then a new support function is proposed to measure the relationship among values in a visibility graph. After that, a weighted network is constructed to determine the weight of each value...
February 2017: Chaos
Weipeng Hu, Mingzhe Song, Zichen Deng, Hailin Zou, Bingqing Wei
The occurrence of chaos in the transverse oscillation of the carbon nanotube in all of the precise micro-nano mechanical systems has a strong impact on the stability and the precision of the micro-nano systems, the conditions of which are related with the boundary restraints of the carbon nanotube. To generalize some transverse oscillation problems of the carbon nanotube studied in current references, the elastic restraints at both ends of the single-walled carbon nanotube are considered by means of rotational and translational springs to investigate the effects of the boundary restraints on the chaotic properties of the carbon nanotube in this paper...
February 2017: Chaos
Jakub Spiechowicz, Marcin Kostur, Jerzy Łuczka
We study diffusion properties of an inertial Brownian motor moving on a ratchet substrate, i.e., a periodic structure with broken reflection symmetry. The motor is driven by an unbiased time-periodic symmetric force that takes the system out of thermal equilibrium. For selected parameter sets, the system is in a non-chaotic regime in which we can identify a non-monotonic dependence of the diffusion coefficient on temperature: for low temperature, it initially increases as the temperature grows, passes through its local maximum, next starts to diminish reaching its local minimum, and finally it monotonically increases in accordance with the Einstein linear relation...
February 2017: Chaos
Vikram Sagar, Yi Zhao
In the present work, the effect of personal behavior induced preventive measures is studied on the spread of epidemics over scale free networks that are characterized by the differential rate of disease transmission. The role of personal behavior induced preventive measures is parameterized in terms of variable λ, which modulates the number of concurrent contacts a node makes with the fraction of its neighboring nodes. The dynamics of the disease is described by a non-linear Susceptible Infected Susceptible model based upon the discrete time Markov Chain method...
February 2017: Chaos
S Etikyala, R I Sujith
In this paper, we report on the existence of the phenomenon of change of criticality in a horizontal Rijke tube, a prototypical thermoacoustic system. In the experiments, the phenomenon is shown to occur as the criticality of the Hopf bifurcation changes with varying air flow rates in the system. The dynamics of a nonlinear system exhibiting Hopf bifurcation can be described using a Stuart-Landau equation (SLE) in the vicinity of the bifurcation point. The criticality of Hopf bifurcations can be determined by the Landau constant of the Stuart-Landau equation, which represents the effect of nonlinearities in the system...
February 2017: Chaos
Ernesto Estrada, Alhanouf Ali Alhomaidhi, Fawzi Al-Thukair
We study a Gaussian matrix function of the adjacency matrix of artificial and real-world networks. We motivate the use of this function on the basis of a dynamical process modeled by the time-dependent Schrödinger equation with a squared Hamiltonian. In particular, we study the Gaussian Estrada index-an index characterizing the importance of eigenvalues close to zero. This index accounts for the information contained in the eigenvalues close to zero in the spectra of networks. Such a method is a generalization of the so-called "Folded Spectrum Method" used in quantum molecular sciences...
February 2017: Chaos
N M Musammil, K Porsezian, P A Subha, K Nithyanandan
We investigate the dynamics of vector dark solitons propagation using variable coefficient coupled nonlinear Schrödinger (Vc-CNLS) equation. The dark soliton propagation and evolution dynamics in the inhomogeneous system are studied analytically by employing the Hirota bilinear method. It is apparent from our asymptotic analysis that the collision between the dark solitons is elastic in nature. The various inhomogeneous effects on the evolution and interaction between dark solitons are explored, with a particular emphasis on nonlinear tunneling...
February 2017: Chaos
Duan Wang, Xin Zhang, Davor Horvatic, Boris Podobnik, H Eugene Stanley
To study the statistical structure of crosscorrelations in empirical data, we generalize random matrix theory and propose a new method of cross-correlation analysis, known as autoregressive random matrix theory (ARRMT). ARRMT takes into account the influence of auto-correlations in the study of cross-correlations in multiple time series. We first analytically and numerically determine how auto-correlations affect the eigenvalue distribution of the correlation matrix. Then we introduce ARRMT with a detailed procedure of how to implement the method...
February 2017: Chaos
Yilun Shang
This paper deals with a hybrid opinion dynamics comprising averager, copier, and voter agents, which ramble as random walkers on a spatial network. Agents exchange information following some deterministic and stochastic protocols if they reside at the same site in the same time. Based on stochastic stability of Markov chains, sufficient conditions guaranteeing consensus in the sense of almost sure convergence have been obtained. The ultimate consensus state is identified in the form of an ergodicity result...
February 2017: Chaos
Sho Shirasaka, Wataru Kurebayashi, Hiroya Nakao
Phase reduction framework for limit-cycling systems based on isochrons has been used as a powerful tool for analyzing the rhythmic phenomena. Recently, the notion of isostables, which complements the isochrons by characterizing amplitudes of the system state, i.e., deviations from the limit-cycle attractor, has been introduced to describe the transient dynamics around the limit cycle [Wilson and Moehlis, Phys. Rev. E 94, 052213 (2016)]. In this study, we introduce a framework for a reduced phase-amplitude description of transient dynamics of stable limit-cycling systems...
February 2017: Chaos
Hai-Qiong Zhao
In this paper, a new semi-discrete integrable combination of Burgers and Sharma-Tasso-Olver equation is investigated. The underlying integrable structures like the Lax pair, the infinite number of conservation laws, the Darboux-Bäcklund transformation, and the solutions are presented in the explicit form. The theory of the semi-discrete equation including integrable properties yields the corresponding theory of the continuous counterpart in the continuous limit. Finally, numerical experiments are provided to demonstrate the effectiveness of the developed integrable semi-discretization algorithms...
February 2017: Chaos
Zuo-Wei Cai, Jian-Hua Huang, Li-Hong Huang
The aim of this paper is to provide a novel switching control design to solve finite-time stabilization issues of a discontinuous or switching dynamical system. In order to proceed with our analysis, we first design two kinds of switching controllers: switching adaptive controller and switching state-feedback controller. Then, we apply the proposed switching control technique to stabilize the states of delayed memristor-based neural networks (DMNNs) in finite time. Based on a famous finite-time stability theorem, the theory of differential inclusion and the generalized Lyapunov functional method, some sufficient conditions are obtained to guarantee the finite-time stabilization control of DMNNs...
February 2017: Chaos
T L Carroll, J M Byers
We describe a method to estimate embedding dimension from a time series. This method includes an estimate of the probability that the dimension estimate is valid. Such validity estimates are not common in algorithms for calculating the properties of dynamical systems. The algorithm described here compares the eigenvalues of covariance matrices created from an embedded signal to the eigenvalues for a covariance matrix of a Gaussian random process with the same dimension and number of points. A statistical test gives the probability that the eigenvalues for the embedded signal did not come from the Gaussian random process...
February 2017: Chaos
Fabio L Traversa, Massimiliano Di Ventra
We introduce a class of digital machines, we name Digital Memcomputing Machines, (DMMs) able to solve a wide range of problems including Non-deterministic Polynomial (NP) ones with polynomial resources (in time, space, and energy). An abstract DMM with this power must satisfy a set of compatible mathematical constraints underlying its practical realization. We prove this by making a connection with the dynamical systems theory. This leads us to a set of physical constraints for poly-resource resolvability. Once the mathematical requirements have been assessed, we propose a practical scheme to solve the above class of problems based on the novel concept of self-organizing logic gates and circuits (SOLCs)...
February 2017: Chaos
Audric Drogoul, Romain Veltz
In this work, we provide three different numerical evidences for the occurrence of a Hopf bifurcation in a recently derived [De Masi et al., J. Stat. Phys. 158, 866-902 (2015) and Fournier and löcherbach, Ann. Inst. H. Poincaré Probab. Stat. 52, 1844-1876 (2016)] mean field limit of a stochastic network of excitatory spiking neurons. The mean field limit is a challenging nonlocal nonlinear transport equation with boundary conditions. The first evidence relies on the computation of the spectrum of the linearized equation...
February 2017: Chaos
Fang Zeng, Xiang Li, Ke Li
The complex topology and adaptive behavior of infrastructure systems are driven by both self-organization of the demand and rigid engineering solutions. Therefore, engineering complex systems requires a method balancing holism and reductionism. To model the growth of water distribution networks, a complex network model was developed following the combination of local optimization rules and engineering considerations. The demand node generation is dynamic and follows the scaling law of urban growth. The proposed model can generate a water distribution network (WDN) similar to reported real-world WDNs on some structural properties...
February 2017: Chaos
Fajun Yu
Starting from a discrete spectral problem, we derive a hierarchy of nonlinear discrete equations which include the Ablowitz-Ladik (AL) equation. We analytically study the discrete rogue-wave (DRW) solutions of AL equation with three free parameters. The trajectories of peaks and depressions of profiles for the first- and second-order DRWs are produced by means of analytical and numerical methods. In particular, we study the solutions with dispersion in parity-time ( PT) symmetric potential for Ablowitz-Musslimani equation...
February 2017: Chaos
Arindam Mishra, Suman Saha, Prodyot K Roy, Tomasz Kapitaniak, Syamal K Dana
We observe the multiclustered oscillation death and chimeralike states in an array of Josephson junctions under a combination of self-repulsive and cross-attractive mean-field interaction when each isolated junction is in a bistable state, a coexisting fixed point and an oscillatory state. We locate the parameter landscape of the multiclustered oscillation death and chimeralike states. Alternatively, a purely repulsive mean-field interaction in an array of all oscillatory junctions produces chimeralike states with signatures of metastability in the incoherent subpopulation of junctions...
February 2017: Chaos
Tessa Rosenberger, Graham Schattgen, Matthew King-Smith, Prakrit Shrestha, Katsuo J Maxted, John F Lindner
We describe the design, construction, and dynamics of low-cost mechanical arrays of 3D-printed bistable elements whose shapes interact with wind to couple them one-way. Unlike earlier hydromechanical unidirectional arrays, our aeromechanical one-way arrays are simpler, easier to study, and exhibit a broader range of phenomena. Solitary waves or solitons propagate in one direction at speeds proportional to wind speeds. Periodic boundaries enable solitons to annihilate in pairs in arrays with an even number of elements...
February 2017: Chaos
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