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Leonhard Lücken, David P Rosin, Vasco M Worlitzer, Serhiy Yanchuk
We consider the recurrent pulse-coupled networks of excitable elements with delayed connections, which are inspired by the biological neural networks. If the delays are tuned appropriately, the network can either stay in the steady resting state, or alternatively, exhibit a desired spiking pattern. It is shown that such a network can be used as a pattern-recognition system. More specifically, the application of the correct pattern as an external input to the network leads to a self-sustained reverberation of the encoded pattern...
January 2017: Chaos
Leandro M Alonso
This article describes a numerical procedure designed to tune the parameters of periodically driven dynamical systems to a state in which they exhibit rich dynamical behavior. This is achieved by maximizing the diversity of subharmonic solutions available to the system within a range of the parameters that define the driving. The procedure is applied to a problem of interest in computational neuroscience: a circuit composed of two interacting populations of neurons under external periodic forcing. Depending on the parameters that define the circuit, such as the weights of the connections between the populations, the response of the circuit to the driving can be strikingly rich and diverse...
January 2017: Chaos
Mustapha Tlidi, Krassimir Panajotov
We demonstrate a way to generate two-dimensional rogue waves in two types of broad area nonlinear optical systems subject to time-delayed feedback: in the generic Lugiato-Lefever model and in the model of a broad-area surface-emitting laser with saturable absorber. The delayed feedback is found to induce a spontaneous formation of rogue waves. In the absence of delayed feedback, spatial pulses are stationary. The rogue waves are exited and controlled by the delay feedback. We characterize their formation by computing the probability distribution of the pulse height...
January 2017: Chaos
D Premraj, K Suresh, Tanmoy Banerjee, K Thamilmaran
The slow passage effect in a dynamical system generally induces a delay in bifurcation that imposes an uncertainty in the prediction of the dynamical behaviors around the bifurcation point. In this paper, we investigate the influence of linear time-delayed self-feedback on the slow passage through the delayed Hopf and pitchfork bifurcations in a parametrically driven nonlinear oscillator. We perform linear stability analysis to derive the Hopf bifurcation point and its stability as a function of self-feedback time delay...
January 2017: Chaos
Igal Berenstein, Jorge Carballido-Landeira
In this paper, we investigate pattern formation in a model of a reaction confined in a microemulsion, in a regime where both Turing and wave instability occur. In one-dimensional systems, the pattern corresponds to spatiotemporal intermittency where the behavior of the systems alternates in both time and space between stationary Turing patterns and traveling waves. In two-dimensional systems, the behavior initially may correspond to Turing patterns, which then turn into wave patterns. The resulting pattern also corresponds to a chaotic state, where the system alternates in both space and time between standing wave patterns and traveling waves, and the local dynamics may show vanishing amplitude of the variables...
January 2017: Chaos
Guangyi Wang, Shouchi Zang, Xiaoyuan Wang, Fang Yuan, Herbert Ho-Ching Iu
Memristors and memcapacitors are two new nonlinear elements with memory. In this paper, we present a Hewlett-Packard memristor model and a charge-controlled memcapacitor model and design a new chaotic oscillator based on the two models for exploring the characteristics of memristors and memcapacitors in nonlinear circuits. Furthermore, many basic dynamical behaviors of the oscillator, including equilibrium sets, Lyapunov exponent spectrums, and bifurcations with various circuit parameters, are investigated theoretically and numerically...
January 2017: Chaos
Kaihua Xi, Johan L A Dubbeldam, Hai Xiang Lin
Synchronization is essential for the proper functioning of power grids; we investigate the synchronous states and their stability for cyclic power grids. We calculate the number of stable equilibria and investigate both the linear and nonlinear stabilities of the synchronous state. The linear stability analysis shows that the stability of the state, determined by the smallest nonzero eigenvalue, is inversely proportional to the size of the network. We use the energy barrier to measure the nonlinear stability and calculate it by comparing the potential energy of the type-1 saddles with that of the stable synchronous state...
January 2017: Chaos
K R Khusnutdinova, M R Tranter
We study the scattering of a long longitudinal radiating bulk strain solitary wave in the delaminated area of a two-layered elastic structure with soft ("imperfect") bonding between the layers within the scope of the coupled Boussinesq equations. The direct numerical modelling of this and similar problems is challenging and has natural limitations. We develop a semi-analytical approach, based on the use of several matched asymptotic multiple-scale expansions and averaging with respect to the fast space variable, leading to the coupled Ostrovsky equations in bonded regions and uncoupled Korteweg-de Vries equations in the delaminated region...
January 2017: Chaos
Päivi Sikiö, Tero Tynjälä, Payman Jalali
In this article, a spatiotemporal dynamical system model (tree model) is utilized for investigating the features of forced and unforced turbulence in a dispersed phase two-phase system. The tree model includes a variable for spatial dimension in addition to variables of wavenumber and time, which display both spatial and temporal intermittencies. The focus of this paper is to study the turbulence modulation due to the presence of rigid particles. The study considers particles with the sizes of 32, 64, and 128 times the Kolmogorov length scale...
January 2017: Chaos
P S Skardal, R Sevilla-Escoboza, V P Vera-Ávila, J M Buldú
We investigate the existence of an optimal interplay between the natural frequencies of a group of chaotic oscillators and the topological properties of the network they are embedded in. We identify the conditions for achieving phase synchronization in the most effective way, i.e., with the lowest possible coupling strength. Specifically, we show by means of numerical and experimental results that it is possible to define a synchrony alignment function J(ω,L) linking the natural frequencies ωi of a set of non-identical phase-coherent chaotic oscillators with the topology of the Laplacian matrix L, the latter accounting for the specific organization of the network of interactions between oscillators...
January 2017: Chaos
Hiroshi Ashikaga, Ryan G James
A spiral wave is a macroscopic dynamics of excitable media that plays an important role in several distinct systems, including the Belousov-Zhabotinsky reaction, seizures in the brain, and lethal arrhythmia in the heart. Because the spiral wave dynamics can exhibit a wide spectrum of behaviors, its precise quantification can be challenging. Here we present a hybrid geometric and information-theoretic approach to quantifying the spiral wave dynamics. We demonstrate the effectiveness of our approach by applying it to numerical simulations of a two-dimensional excitable medium with different numbers and spatial patterns of spiral waves...
January 2017: Chaos
Qintao Gan
In this paper, the exponential synchronization problem of generalized reaction-diffusion neural networks with mixed time-varying delays is investigated concerning Dirichlet boundary conditions in terms of p-norm. Under the framework of the Lyapunov stability method, stochastic theory, and mathematical analysis, some novel synchronization criteria are derived, and an aperiodically intermittent control strategy is proposed simultaneously. Moreover, the effects of diffusion coefficients, diffusion space, and stochastic perturbations on the synchronization process are explicitly expressed under the obtained conditions...
January 2017: Chaos
Ilan Koren, Eli Tziperman, Graham Feingold
Marine stratocumulus cloud decks are regarded as the reflectors of the climate system, returning back to space a significant part of the income solar radiation, thus cooling the atmosphere. Such clouds can exist in two stable modes, open and closed cells, for a wide range of environmental conditions. This emergent behavior of the system, and its sensitivity to aerosol and environmental properties, is captured by a set of nonlinear equations. Here, using linear stability analysis, we express the transition from steady to a limit-cycle state analytically, showing how it depends on the model parameters...
January 2017: Chaos
Christian L E Franzke
Extreme events capture the attention and imagination of the general public. Extreme events, especially meteorological and climatological extremes, cause significant economic damages and lead to a significant number of casualties each year. Thus, the prediction of extremes is of obvious importance. Here, I will survey the predictive skill and the predictability of extremes using dynamic-stochastic models. These dynamic-stochastic models combine deterministic nonlinear dynamics with a stochastic component, which consists potentially of both additive and multiplicative noise components...
January 2017: Chaos
Nilaj Chakrabarty, Aditya Jain, Nijil Lal, Kantimay Das Gupta, Punit Parmananda
In this paper, we present an experimental setup and an associated mathematical model to study the synchronization of two self-sustained, strongly coupled, mechanical oscillators (metronomes). The effects of a small detuning in the internal parameters, namely, damping and frequency, have been studied. Our experimental system is a pair of spring wound mechanical metronomes; coupled by placing them on a common base, free to move along a horizontal direction. We designed a photodiode array based non-contact, non-magnetic position detection system driven by a microcontroller to record the instantaneous angular displacement of each oscillator and the small linear displacement of the base, coupling the two...
January 2017: Chaos
Manuela A D Aguiar, Ana Paula S Dias, Flora Ferreira
We consider feed-forward and auto-regulation feed-forward neural (weighted) coupled cell networks. In feed-forward neural networks, cells are arranged in layers such that the cells of the first layer have empty input set and cells of each other layer receive only inputs from cells of the previous layer. An auto-regulation feed-forward neural coupled cell network is a feed-forward neural network where additionally some cells of the first layer have auto-regulation, that is, they have a self-loop. Given a network structure, a robust pattern of synchrony is a space defined in terms of equalities of cell coordinates that is flow-invariant for any coupled cell system (with additive input structure) associated with the network...
January 2017: Chaos
Guochao Wang, Jun Wang
We make an approach on investigating the fluctuation behaviors of financial volatility duration dynamics. A new concept of volatility two-component range intensity (VTRI) is developed, which constitutes the maximal variation range of volatility intensity and shortest passage time of duration, and can quantify the investment risk in financial markets. In an attempt to study and describe the nonlinear complex properties of VTRI, a random agent-based financial price model is developed by the finite-range interacting biased voter system...
January 2017: Chaos
Xin Li, Zhenya Yan
We explore the parity-time-( PT)-symmetric optical couplers with the cubic both self- and cross-interactions corresponding to self- and cross-phase modulations. When the coefficient of the cubic cross-interaction is chosen as the different values, we find three distinct cases for two branches, including the stable-stable modes (linear unbroken PT-symmetric phase), stable-unstable modes (linear unbroken PT-symmetric phase), as well as unstable-unstable modes (linear broken PT-symmetric phase). Moreover, we find the periodic trajectories for some parameters...
January 2017: Chaos
Lei Liu, Bo Tian, Xi-Yang Xie, Yue-Yang Guan
Studied in this paper are the vector bright solitons of the coupled higher-order nonlinear Schrödinger system, which describes the simultaneous propagation of two ultrashort pulses in the birefringent or two-mode fiber. With the help of auxiliary functions, we obtain the bilinear forms and construct the vector bright one- and two-soliton solutions via the Hirota method and symbolic computation. Two types of vector solitons are derived. Single-hump, double-hump, and flat-top solitons are displayed. Elastic and inelastic interactions between the Type-I solitons, between the Type-II solitons, and between the two combined types of the solitons are revealed, respectively...
January 2017: Chaos
Lian Duan, Lihong Huang, Xianwen Fang
In this paper, we study the finite-time synchronization problem for recurrent neural networks with discontinuous activations and time-varying delays. Based on the finite-time convergence theory and by using the nonsmooth analysis technique, some finite-time synchronization criteria for the considered neural network model are established, which are new and complement some existing ones. The feasibility and effectiveness of the proposed synchronization method are supported by two examples with numerical simulations...
January 2017: Chaos
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