On the validity of memristor modeling in the neural network literature

An analysis of the literature shows that there are two types of non-memristive models that have been widely used in the modeling of so-called "memristive" neural networks. Here, we demonstrate that such models have nothing in common with the concept of memristive elements: they describe either non-linear resistors or certain bi-state systems, which all are devices without memory. Therefore, the results presented in a significant number of publications are at least questionable, if not completely irrelevant to the actual field of memristive neural networks

Transition from anticipatory to lag synchronization via complete synchronization in time-delay systems

The existence of anticipatory, complete and lag synchronization in a single system having two different time-delays, that is feedback delay $\tau_1$ and coupling delay $\tau_2$, is identified. The transition from anticipatory to complete synchronization and from complete to lag synchronization as a function of coupling delay $\tau_2$ with suitable stability condition is discussed. The existence of anticipatory and lag synchronization is characterized both by the minimum of similarity function and the transition from on-off intermittency to periodic structure in laminar phase distribution.Comment: 14 Pages and 12 Figure

Isochronal synchronization of delay-coupled systems

We consider small network models for mutually delay-coupled systems which typically do not exhibit stable isochronally synchronized solutions. We show that for certain coupling architectures which involve delayed self feedback to the nodes, the oscillators become isochronally synchronized. Applications are shown for both incoherent pump coupled lasers and spatio-temporal coupled fiber ring lasers.Comment: 5 pages, accepted for publication in Physical Review

Exponential Lag Synchronization of Cohen-Grossberg Neural Networks with Discrete and Distributed Delays on Time Scales

In this article, we investigate exponential lag synchronization results for the Cohen-Grossberg neural networks (C-GNNs) with discrete and distributed delays on an arbitrary time domain by applying feedback control. We formulate the problem by using the time scales theory so that the results can be applied to any uniform or non-uniform time domains. Also, we provide a comparison of results that shows that obtained results are unified and generalize the existing results. Mainly, we use the unified matrix-measure theory and Halanay inequality to establish these results. In the last section, we provide two simulated examples for different time domains to show the effectiveness and generality of the obtained analytical results.Comment: 20 pages, 18 figure

Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators

A chimera state is a spatio-temporal pattern in a network of identical coupled oscillators in which synchronous and asynchronous oscillation coexist. This state of broken symmetry, which usually coexists with a stable spatially symmetric state, has intrigued the nonlinear dynamics community since its discovery in the early 2000s. Recent experiments have led to increasing interest in the origin and dynamics of these states. Here we review the history of research on chimera states and highlight major advances in understanding their behaviour.Comment: 26 pages, 3 figure

General decay lag anti-synchronization of multi-weighted delayed coupled neural networks with reaction–diffusion terms

We propose a new anti-synchronization concept, called general decay lag anti-synchronization, by combining the definitions of decay synchronization and lag synchronization. Novel criteria for the decay lag anti-synchronization of multi-weighted delayed coupled reaction–diffusion neural networks (MWDCRDNNs) with and without bounded distributed delays are derived by constructing an appropriate nonlinear controller and using the Lyapunov functional method. Moreover, the robust decay lag anti-synchronization of MWDCRDNNs with and without bounded distributed delays is considered. Finally, two numerical simulations are performed to validate the obtained results

Synchronicity From Synchronized Chaos

The synchronization of loosely coupled chaotic oscillators, a phenomenon investigated intensively for the last two decades, may realize the philosophical notion of synchronicity. Effectively unpredictable chaotic systems, coupled through only a few variables, commonly exhibit a predictable relationship that can be highly intermittent. We argue that the phenomenon closely resembles the notion of meaningful synchronicity put forward by Jung and Pauli if one identifies "meaningfulness" with internal synchronization, since the latter seems necessary for synchronizability with an external system. Jungian synchronization of mind and matter is realized if mind is analogized to a computer model, synchronizing with a sporadically observed system as in meteorological data assimilation. Internal synchronization provides a recipe for combining different models of the same objective process, a configuration that may also describe the functioning of conscious brains. In contrast to Pauli's view, recent developments suggest a materialist picture of semi-autonomous mind, existing alongside the observed world, with both exhibiting a synchronistic order. Basic physical synchronicity is manifest in the non-local quantum connections implied by Bell's theorem. The quantum world resides on a generalized synchronization "manifold", a view that provides a bridge between nonlocal realist interpretations and local realist interpretations that constrain observer choice .Comment: 1) clarification regarding the connection with philosophical synchronicity in Section 2 and in the concluding section 2) reference to Maldacena-Susskind "ER=EPR" relation in discussion of role of wormholes in entanglement and nonlocality 3) length reduction and stylistic changes throughou

Delay time modulation induced oscillating synchronization and intermittent anticipatory/lag and complete synchronizations in time-delay nonlinear dynamical systems

Existence of a new type of oscillating synchronization that oscillates between three different types of synchronizations (anticipatory, complete and lag synchronizations) is identified in unidirectionally coupled nonlinear time-delay systems having two different time-delays, that is feedback delay with a periodic delay time modulation and a constant coupling delay. Intermittent anticipatory, intermittent lag and complete synchronizations are shown to exist in the same system with identical delay time modulations in both the delays. The transition from anticipatory to complete synchronization and from complete to lag synchronization as a function of coupling delay with suitable stability condition is discussed. The intermittent anticipatory and lag synchronizations are characterized by the minimum of similarity functions and the intermittent behavior is characterized by a universal asymptotic $-{3/2}$ power law distribution. It is also shown that the delay time carved out of the trajectories of the time-delay system with periodic delay time modulation cannot be estimated using conventional methods, thereby reducing the possibility of decoding the message by phase space reconstruction.Comment: accepted for publication in CHAOS, revised in response to referees comment