Noise-induced synchronization in bidirectionally coupled type-I neurons

We present here some studies on noise-induced order and synchronous firing in a system of bidirectionally coupled generic type-I neurons. We find that transitions from unsynchronized to completely synchronized states occur beyond a critical value of noise strength that has a clear functional dependence on neuronal coupling strength and input values. For an inhibitory-excitatory (IE) synaptic coupling, the approach to a partially synchronized state is shown to vary qualitatively depending on whether the input is less or more than a critical value. We find that introduction of noise can cause a delay in the bifurcation of the firing pattern of the excitatory neuron for IE coupling.     

Isochronous synchronization in mutually coupled chaotic circuits

This paper examines the robustness of isochronous synchronization in simple arrays of bidirectionally coupled systems. First, the achronal synchronization of two mutually chaotic circuits, which are coupled with delay, is analyzed. Next, a third chaotic circuit acting as a relay between the previous two circuits is introduced. We observe that, despite the delay in the coupling path, the outer dynamical systems show isochronous synchronization of their outputs, i.e., display the same dynamics at exactly the same moment. Finally, we give here the first experimental evidence that the central relaying system is not required to be of the same kind of its outer counterparts.     

Noise-induced synchronization and coherence resonance of a Hodgkin-Huxley model of thermally sensitive neurons

We study nontrivial effects of noise on synchronization and coherence of a chaotic Hodgkin-Huxley model of thermally sensitive neurons. We demonstrate that identical neurons which are not coupled but subjected to a common fluctuating input (Gaussian noise) can achieve complete synchronization when the noise amplitude is larger than a threshold. For nonidentical neurons, noise can induce phase synchronization. Noise enhances synchronization of weakly coupled neurons. We also find that noise enhances the coherence of the spike trains. A saddle point embedded in the chaotic attractor is responsible for these nontrivial noise-induced effects. Relevance of our results to biological information processing is discussed.     

Complex transitions between spike,burst or chaos synchronization states in coupled neurons with coexisting bursting patterns

We investigated the synchronization dynamics of a coupled neuronal system composed of two identical Chay model neurons. The Chay model showed coexisting period-1 and period-2 bursting patterns as a parameter and initial values are varied. We simulated multiple periodic and chaotic bursting patterns with non-(NS), burst phase(BS), spike phase(SS),complete(CS), and lag synchronization states. When the coexisting behavior is near period-2 bursting, the transitions of synchronization states of the coupled system follows very complex transitions that begins with transitions between BS and SS, moves to transitions between CS and SS, and to CS. Most initial values lead to the CS state of period-2 bursting while only a few lead to the CS state of period-1 bursting. When the coexisting behavior is near period-1 bursting, the transitions begin with NS, move to transitions between SS and BS, to transitions between SS and CS, and then to CS. Most initial values lead to the CS state of period-1 bursting but a few lead to the CS state of period-2 bursting. The BS was identified as chaos synchronization. The patterns for NS and transitions between BS and SS are insensitive to initial values. The patterns for transitions between CS and SS and the CS state are sensitive to them. The number of spikes per burst of non-CS bursting increases with increasing coupling strength. These results not only reveal the initial value- and parameterdependent synchronization transitions of coupled systems with coexisting behaviors, but also facilitate interpretation of various bursting patterns and synchronization transitions generated in the nervous system with weak coupling strength.     

Chaotic synchronization through coupling strategies

Usually, complete synchronization (CS) is regarded as the form of synchronization proper of identical chaotic systems, while generalized synchronization (GS) extends CS in nonidentical systems. However, this generally accepted view ignores the role that the coupling plays in determining the type of synchronization. In this work, we show that by choosing appropriate coupling strategies, CS can be observed in coupled chaotic systems with parameter mismatch, and GS can also be achieved in coupled identical systems. Numerical examples are provided to demonstrate these findings. Moreover, experimental verification based on electronic circuits has been carried out to support the numerical results. Our work provides a method to obtain robust CS in synchronization-based chaos communications.     

Coherence Resonance and Noise-Induced Synchronization in Hindmarsh-Rose Neural Network with Different Topologies

In this paper, we investigate coherence resonance （CR） and noise-induced synchronization in Hindmarsh- Rose （HR） neural network with three different types of topologies： regular, random, and small-world. It is found that the additive noise can induce CR in HR neural network with different topologies and its coherence is optimized by a proper noise level. It is also found that as coupling strength increases the plateau in the measure of coherence curve becomes broadened and the effects of network topology is more pronounced simultaneously. Moreover, we find that increasing the probability p of the network topology leads to an enhancement of noise-induced synchronization in HR neurons network.     

Synchronization and control of chaos in coupled chaotic multimode Nd:YAG lasers

In this Letter we numerically investigate the dynamics of a system of two coupled chaotic multimode Nd:YAG lasers with two mode and three mode outputs. Unidirectional and bidirectional coupling schemes are adopted; intensity time series plots, phase space plots and synchronization plots are used for studying the dynamics. Quality of synchronization is measured using correlation index plots. It is found that for laser with two mode output bidirectional direct coupling scheme is found to be effective in achieving complete synchronization, control of chaos and amplification in output intensity. For laser with three mode output, bidirectional difference coupling scheme gives much better chaotic synchronization as compared to unidirectional difference coupling but at the cost of higher coupling strength. We also conclude that the coupling scheme and system properties play an important role in determining the type of synchronization exhibited by the system.     

Thermodynamic and magnetic properties of the hexagonal type Ising nanowire

wIn this paper, the role of multiplicative noise in synchronization of bidirectionally coupled chain is studied. For coupled chain with three nodes, we demonstrate that noise plays positive role in synchronization based on stability theory of stochastic differential equation, and numerical simulations show the theoretical results is correct. For coupled chain with more than three nodes, we discuss the noise’s effect on synchronization by numerical simulations. By the numerical results, one may conjecture that the noise also have positive effect on synchronization when node number is larger than three. However, the positive effect of noise on synchronization is weaken with node number increasing.     

Crowd synchrony and quorum sensing in delay-coupled lasers

Crowd synchrony and quorum sensing arise when a large number of dynamical elements communicate with each other via a common information pool. Previous evidence has shown that this type of coupling leads to synchronization, when coupling is instantaneous and the number of coupled elements is large enough. Here we consider a situation in which the transmission of information between the system components and the coupling pool is not instantaneous. To that end, we model a system of semiconductor lasers optically coupled to a central laser with a delay. Our results show that, even though the lasers are nonidentical due to their distinct optical frequencies, zero-lag synchronization arises. By changing a system parameter, we can switch between two different types of synchronization transition. The dependence of the transition with respect to the delay-coupling parameters is studied.     

Impact of delays and rewiring on the dynamics of small-world neuronal networks with two types of coupling

We study synchronization transitions and pattern formation on small-world networks consisting of Morris-Lecar excitable neurons in dependence on the information transmission delay and the rewiring probability. In addition, networks formed via gap junctional connections and coupling via chemical synapses are considered separately. For gap-junctionally coupled networks we show that short delays can induce zigzag fronts of excitations, whereas long delays can further detriment synchronization due to a dynamic clustering anti-phase synchronization transition. For the synaptically coupled networks, on the other hand, we find that the clustering anti-phase synchronization can appear as a direct consequence of the prolongation of information transmission delay, without being accompanied by zigzag excitatory fronts. Irrespective of the coupling type, however, we show that an appropriate small-world topology can always restore synchronized activity if only the information transmission delays are short or moderate at most. Long information transmission delays always evoke anti-phase synchronization and clustering, in which case the fine-tuning of the network topology fails to restore the synchronization of neuronal activity.     

Inverse synchronization of coupled fractional-order systems through open-plus-closed-loop control

In this paper, the inverse synchronization problem of fractional-order dynamical systems is investigated. A general explicit coupling via an open-plus-closed-loop control for inverse synchronization of two arbitrary unidirectionally or bidirectionally coupled fractional-order systems is proposed. The inverse synchronization is proved analytically based on the stability theorem of the fractional differential equations. A key feature of this proposed scheme is that it can be applied not only to nonchaotic but also to chaotic fractional-order systems whenever they exhibit regular or irregular oscillations. Feasibility of the proposed inverse synchronization scheme is illustrated through numerical simulations.     

Dynamic synchronization of a time-evolving optical network of chaotic oscillators

We present and experimentally demonstrate a technique for achieving and maintaining a global state of identical synchrony of an arbitrary network of chaotic oscillators even when the coupling strengths are unknown and time-varying. At each node an adaptive synchronization algorithm dynamically estimates the current strength of the net coupling signal to that node. We experimentally demonstrate this scheme in a network of three bidirectionally coupled chaotic optoelectronic feedback loops and we present numerical simulations showing its application in larger networks. The stability of the synchronous state for arbitrary coupling topologies is analyzed via a master stability function approach.     

Nonequilibrium potential for arbitrary-connected networks of FitzHugh-Nagumo elements

We study an array of N units with FitzHugh-Nagumo dynamics linearly coupled. The system is submitted to a subthreshold harmonic signal and independent Gaussian white noises with a common intensity η. In the limit of adiabatic driving, we analytically calculate the system’s nonequilibrium potential for arbitrary linear coupling. We illustrate its applicability by investigating noise-induced effects in an excitable regular network with extended antiphase coupling. In particular, the levels of noise for short-wavelength phase-instability, network’s synchronization and depinning of “defects” (groups of contiguous inhibited neurons on an antiphase background) are theoretically predicted and numerically confirmed. The origin of these collective effects and the dependence with parameters of the most probable length of defects are explained in terms of the system’s nonequilibrium potential.     

Enhanced Synchronization of Intercellular Calcium Oscillations by Noise Contaminated Signals

We consider the dynamics of locally coupled calcium oscillation systems, each cell is subjected to extracellular contaminated signal, which contains common sub-threshold signal and independent Gaussian noise. It is found that intermediate noise can enhance synchronized oscillations of calcium ions, where the frequency of noise-induced oscillations is matched with the one of sub-threshold external signal. We show that synchronization is enhanced as a result of the entrainment of external signal. Furthermore, the effect of coupling strength is considered. We find above-mentioned phenomenon exists only when coupling strength is very small. Our findings may exhibit that noise can enhance the detection of feeble external signal through the mechanism of synchronization of intercellular calcium ions.     

Transition to complete synchronization via near-synchronization in two coupled chaotic neurons

The synchronization transition in two coupled chaotic Morris-Lecar （ML） neurons with gap junction is studied with the coupling strength increasing. The conditional Lyapunov exponents, along with the synchronization errors are calculated to diagnose synchronization of two coupled chaotic ML neurons. As a result, it is shown that the increase in the coupling strength leads to incoherence, then induces a transition process consisting of three different synchronization states in succession, namely, burst synchronization, near-synchronization and embedded burst synchronization, and achieves complete synchronization of two coupled neurons finally. These sequential transitions to synchronization reveal a new transition route from incoherence to complete synchronization in coupled systems with multi-time scales.     

The effect of finite response–time in coupled dynamical systems

The paper investigates synchronization in unidirectionally coupled dynamical systems wherein the influence of drive on response is cumulative: coupling signals are integrated over a time interval τ. A major consequence of integrative coupling is that the onset of the generalized and phase synchronization occurs at higher coupling compared to the instantaneous (τ?=?0) case. The critical coupling strength at which synchronization sets in is found to increase with τ. The systems explored are the chaotic Rössler and limit cycle (the Landau–Stuart model) oscillators. For coupled Rössler oscillators the region of generalized synchrony in the phase space is intercepted by an asynchronous region which corresponds to anomalous generalized synchronization.     

Synchronization by dynamical relaying in electronic circuit arrays

We experimentally study the synchronization of two chaotic electronic circuits whose dynamics is relayed by a third parameter-matched circuit, to which they are coupled bidirectionally in a linear chain configuration. In a wide range of operating parameters, this setup leads to synchronization between the outer circuits, while the relaying element remains unsynchronized. The specifics of the synchronization differ with the coupling level: for low couplings a state of intermittent synchronization between the outer circuits coexists with one of antiphase synchronization. Synchronization becomes in phase for moderate couplings, and for strong coupling identical synchronization is observed between the outer elements, which are themselves synchronized in a generalized way with the relaying element. In the latter situation, the middle element displays a triple-scroll attractor that is not possible to obtain when the chaotic oscillator is isolated.     

Coupling induced logical stochastic resonance

In this work we will demonstrate the following result: when we have two coupled bistable sub-systems, each driven separately by an external logic input signal, the coupled system yields outputs that can be mapped to specific logic gate operations in a robust manner, in an optimal window of noise. So, though the individual systems receive only one logic input each, due to the interplay of coupling, nonlinearity and noise, they cooperatively respond to give a logic output that is a function of both inputs. Thus the emergent collective response of the system, due to the inherent coupling, in the presence of a noise floor, maps consistently to that of logic outputs of the two inputs, a phenomenon we term coupling induced Logical Stochastic Resonance. Lastly, we demonstrate our idea in proof of principle circuit experiments.     

Burst synchronization of electrically and chemically coupled map-based neurons

Burst synchronization and burst dynamics of a system consisting of two map-based neurons coupled through electrical or chemical synapses are discussed. Some basic characteristic quantities are introduced to describe burst synchronization and burst dynamics of neurons. It is observed that excitatory coupling leads to in-phase burst synchronization but inhibitory coupling results in anti-phase one. By using the basic characteristics of burst dynamics, the effects of the intrinsic bursting properties and the coupling schemes on complex bursting behaviors are also presented for both inhibitory and excitatory couplings. The results are instructive to identify bursting behaviors through experimental data.     

Phase-lag synchronization analysis in complex systems with directed inter-relations

In this work, we proposed a novel way to estimate phase-lag synchronization in coupled systems. This approach was applied into two systems: a directed-coupled Rössler-Lorenz system and a network of Izhikevich neurons. For the former case, the phase-lag synchronization revealed an increase in complexity for the Lorenz subsystem components, when the coupling is activated. The opposite behavior was observed when the Izhikevich network were organized in a hierarchical way. Our results point out to emergent synchronism related to causal interactions in coupled complex systems.