Mean-field Coupling Research Articles

Spontaneous Magnetization Induced by Antiferromagnetic Toroidal Ordering.

The magnetic toroidal dipole moment, which is induced by a vortex-type spin texture, manifests itself in parity-breaking physical phenomena, such as a linear magnetoelectric effect and nonreciprocal transport. We elucidate that a staggered alignment of the magnetic toroidal dipole can give rise to spontaneous magnetization even under antiferromagnetic structures. We demonstrate the emergence of uniform magnetization by considering the collinear antiferromagnetic structure with the staggered magnetic toroidal dipole moment on a bilayer zigzag chain. Based on the model calculations, we show that the interplay between the collinear antiferromagnetic mean field and relativistic spin-orbit coupling plays an important role in inducing the magnetization.

Explosive and semi-explosive transitions in parametrically perturbed systems

The phenomenon of transition between steady states, namely amplitude death and oscillation death, is identified in certain models of coupled parametrically driven nonlinear oscillators. Intriguingly, the nature of the transition is explosive. It is significant to note that this observation of explosive transition has been made in systems of identical coupled oscillators with repulsive mean-field coupling. In particular, we find that when the coupling strength increases, there are semi-explosive transitions in parametrically perturbed duffing oscillators and explosive transitions in parametrically perturbed van der Pol oscillators. We obtain analytical expressions for the critical bifurcation points through linear stability analysis. Detailed numerical studies have been performed to confirm the phenomenon.

Emergence of chimera states in neural networks with distance-dependent mean field coupling

The emergence of chimera states in neural networks has been an interesting area of research in the past few years and aims to explore the complex brain functions. Even though the presence of chimera states in systems with nonlocal interaction is well known, its emergence in networks with global and local interactions is least explored. Different techniques like introducing distance dependent interactions and restricting initial conditions to certain classes are adopted to induce chimera states in such network. This work analyzes methods to induce chimera or multichimera states in a network of mean field coupled Hindmarsh–Rose neurons in ring topology. The interaction schemes in the network, viz., global, nonlocal and local are realized by limiting the number of neurons involved in coupling and the power law exponent gives a distance gradient effect to them. The studies have shown that, in global interaction, power law exponent induces chimera states and reduces the amount of synchrony in the network. The nonlocal coupling is self-capable of inducing chimera states and power law exponent enhances the capability. When the value of power law exponent is high, the synchrony level is independent of the number of neurons taking part in the coupling. The traveling chimera states are induced in the local (nearest neighbor) coupling by modifying the initial conditions.

Diverse phase transitions in Kuramoto model with adaptive mean-field coupling breaking the rotational symmetry

We consider the paradigmatic Kuramoto oscillators coupled via an adaptive mean-field variable that breaks the rotational symmetry. The evolution equation for the mean-field variable is governed by the linear ordinary differential equation corresponding to a low-pass filter with a time-scale parameter, which attenuates the mean-field signal by filtering its high frequency components. We find distinct phase transitions among the incoherent state, standing wave state and synchronized stationary state in both forward and reverse traces in the entire range of the time-scale parameter. In particular, one can observe two distinct continuous transitions, a continuous transition followed by a discontinuous transition, or a single discontinuous transition among the distinct dynamical states in the forward trace depending on the range of the time-scale parameter, which determines the degree of attenuation. Further, one can also observe two distinct continuous transitions or a single discontinuous desynchronization transition in the reverse trace depending on the time-scale parameter. We derive the evolution equations for the macroscopic order parameters governing the dynamics of the discrete set of coupled phase oscillators. We also deduce the analytical conditions for the stability of the Hopf, pitchfork and saddle–node bifurcations, and find them to be in consistent with the dynamical transitions observed using the simulation.

Impact of coupling on neuronal extreme events: Mitigation and enhancement

We focus on the emergence of extreme events in a collection of aperiodic neuronal maps, under local diffusive coupling, as well as global mean-field coupling. Our central finding is that local diffusive coupling enhances the probability of occurrence of both temporal and spatial extreme events, while in marked contrast, global mean-field coupling suppresses extreme events. So the nature of the coupling crucially determines whether the extreme events are enhanced or mitigated by coupling. Further, in globally coupled systems, there exist initial states in a window of coupling strength that exhibit spatial extreme events, but not temporal extreme events, suggesting that spatial extreme events do not imply temporal extreme events. We also explored the existence of discernible patterns in the return maps of successive inter-event intervals in order to gauge short-term risk-assessment. We find that single neuronal maps, as well as systems under strong diffusive coupling, display broad noisy patterns in these return maps, with clusters around characteristic intervals, allowing some short-term predictability in the extreme event sequence. In contrast, under weak diffusive coupling and global coupling, inter-event intervals lose all perceptible correlations, and the distribution extends to very large inter-event intervals. Lastly, we investigated a non-local diffusive coupling form. Interestingly, this coupling yielded a large window where temporal extreme events occurred, but the spatial profile was synchronized, namely, we found synchronized temporal extreme events. Such synchronized extreme spiking is reminiscent of the neuronal activity leading to epileptic seizures and is of potential relevance to extreme events in brain activity.

Exponentially Long Transient Time to Synchronization of Coupled Chaotic Circle Maps in Dense Random Networks.

We study the transition to synchronization in large, dense networks of chaotic circle maps, where an exact solution of the mean-field dynamics in the infinite network and all-to-all coupling limit is known. In dense networks of finite size and link probability of smaller than one, the incoherent state is meta-stable for coupling strengths that are larger than the mean-field critical coupling. We observe chaotic transients with exponentially distributed escape times and study the scaling behavior of the mean time to synchronization.

Dispersal engendered synchronization and stability of mediated infectious diseases in the patchy environment using mean-field diffusive coupling

Mobility of humans and mediating agents significantly affects the scope of mediated infectious diseases. The spatial transmission of mediated infectious diseases ultimately depends on the movement of hosts and mediators. To comprehend the causes, predict, evaluate, and restrict epidemic transmission, it is crucial to investigate the dynamics of mediated infectious diseases in the presence of mobility. The network of mediators and the host metapopulation are related to the spatial coupling for disease dissemination. Thus, in this article, the metapopulation dynamics of the mediated infectious disease model is studied in a patchy environment where the hosts and mediators population is divided into sub-population. Two networks are used to represent the patchy environment: the hosts or humans network and the mediators network. Mean field diffusive coupling is used to connect the network patches. Both homogeneous and heterogeneous networks are investigated in terms of dynamics. Dispersal engenders the patches of corresponding networks to synchronize and reach bistable states of non-trivial amplitude death. Numerical simulations are performed to demonstrate the change from one state to another state, caused by transcritical bifurcation. The stability of disease free equilibrium and endemic equilibrium is also determined by the reproduction number R0.

Multistable chimera states in a smallest population of three coupled oscillators.

We uncover the emergence of distinct sets of multistable chimera states in addition to chimera death and synchronized states in a smallest population of three globally coupled oscillators with mean-field diffusive coupling. Sequence of torus bifurcations result in the manifestation of distinct periodic orbits as a function of the coupling strength, which in turn result in the genesis of distinct chimera states constituted by two synchronized oscillators coexisting with an asynchronous oscillator. Two subsequent Hopf bifurcations result in homogeneous and inhomogeneous steady states resulting in desynchronized steady states and chimera death state among the coupled oscillators. The periodic orbits and the steady states lose their stability via a sequence of saddle-loop and saddle-node bifurcations finally resulting in a stable synchronized state. We have generalized these results to N coupled oscillators and also deduced the variational equationscorresponding to the perturbation transverse to the synchronization manifold and corroborated the synchronized state in the two-parameter phase diagrams using its largest eigenvalue. Chimera states in three coupled oscillators emerge as a solitary state in N coupled oscillator ensemble.

Explosive death transitions in complex networks of limit cycle and chaotic systems

The conditions for explosive death transitions in complex networks of oscillators having generalized network topology, coupled via mean-field diffusion, are derived analytically. The network behaviour is characterized using three order parameters that define the average amplitude of oscillations, the mean state and the fraction of dead oscillators. As the mean field coupling is changed adiabatically, the amplitude order parameter undergoes explosive death transitions and the nodes in the network collectively cease to oscillate. The transition points in the parameter space and the boundaries of amplitude death regime are derived analytically. Sub-critical Hopf bifurcations are shown to be responsible for amplitude death transition. Explosive death transitions are characterized by hysteresis on adiabatic change of the bifurcation parameter and surprisingly, the backward transition point is shown to be independent of network topology. The theoretical developments have been validated through numerical examples, involving networks of limit cycle systems — such as the Van der Pol oscillator and chaotic systems, such as the Rossler attractor for both random and small world networks.

AI-Based Mean Field Game against Resource-Consuming Attacks in Edge Computing

With the rapid development of edge computing, a new paradigm has formed for providing the nearest end service close to the data source. However, insufficient supply of resources makes edge computing devices vulnerable to attacks, especially sensitive to resource-consuming attacks. This article first designs system function module, aiming to deal with resource-consuming attacks based on the general three-layer architecture of edge computing. Combined with the mean field game, an anti-attack model is designed to transform the security defense problem of large terminal-edge-cloud devices into the mean field countermeasure problem, and the self-organizing neural network is used to approximate the mean field coupling equation. On this basis, a distributed AI-driven resource-consuming attack security defense (ARASD) algorithm is designed to obtain the optimal solution for devices security interaction, thereby improving the system’s anti-attack ability. Finally, the effectiveness of the self-organizing neural network is verified through numerical simulation, and the parameters such as the number of initial terminal-edge-cloud devices and the number of iterations of different security defense algorithms are evaluated. The results show that the ARASD algorithm can achieve better resistance to resource-consuming attacks than other state-of-the-art algorithms in a large-scale edge computing architecture.

Evolution and distribution of the anode overpotential and its oscillations in a polymer electrolyte membrane fuel cell exposed to carbon monoxide

Carbon monoxide (CO) poisoning of polymer electrolyte membrane fuel cells (PEMFCs) remains a challenge for their deployment, and a deeper understanding of the spatiotemporal dynamics involved is needed to develop effective mitigation strategies. In this work, localised reference electrodes were used to measure the anode overpotential at three locations across the active area of a galvanostatically operated cell (0.3 A cm−2) exposed to 100 ppm CO/H2. The anode region closest to the inlet was poisoned more rapidly than the rest of the cell, following a sigmoidal variation, and presented a higher CO coverage. The varying CO concentration, combined with local operating conditions, had a direct impact on the distribution of CO coverage. Additionally, complex self-sustained oscillations of the cell voltage and the anode overpotential were observed and correlated with the rate of CO oxidation in the overall cell. The coexistence of a dominant mean-field coupling area closer to the anode inlet, and a dominant migration coupling region closer to the outlet was identified, consistent with reported modelling predictions for a single straight channel cell. Finally, the cell recovery with pure H2 was shown to be a faster process than the CO adsorption, which follows first-order kinetics and is affected by local conditions.

Phase frustration induced remote synchronization.

Remote synchronization (RS) may take an important role in brain functioning and its study has attracted much attention in recent years. So far, most studies of RS are focused on the Stuart-Landau oscillators with mean-field coupling. However, realistic cases may have more complicated couplings and behaviors, such as the brain networks. To make the study of RS a substantial progress toward realistic situations, we here present a model of RS with phase frustration and show that RS can be induced for those systems where no RS exists when there is no phase frustration. By numerical simulations on both the Stuart-Landau and Kuramoto oscillators, we find that the optimal range of RS depends on the match of phase frustrations between the hub and leaf nodes and a fixed relationship of this match is figured out. While for the non-optimal range of RS, we find that RS exists only in a linear band between the phase frustrations of the hub and leaf nodes. A brief theoretical analysis is provided to explain these results.

Explosive synchronization in coupled nonlinear oscillators on multiplex network

We report the emergence of explosive synchronization in a multiplex network where oscillators on the first layer are coupled with attractive coupling and those on the second layer, coupled with repulsive coupling. With Stuart-Landau and FitzHugh-Nagumo oscillators as the nodal dynamics, we consider non-local and mean-field intralayer couplings. We establish that explosive synchronization occurs in the multiplex network in the presence of Gaussian noise, and the transition is first order with hysteresis to a state of complete intra-layer and in-phase interlayer synchronization. The width of the hysteresis depends on the range of intralayer attractive coupling, strength of interlayer coupling and noise. We also see how to have control over this induced transition so that the explosive nature, if undesirable, can be converted to continuous type by tuning the strength of repulsive coupling or noise.

Self-Consistent Transfer Operators: Invariant Measures, Convergence to Equilibrium, Linear Response and Control of the Statistical Properties

We describe a general approach to the theory of self consistent transfer operators. These operators have been introduced as tools for the study of the statistical properties of a large number of all to all interacting dynamical systems subjected to a mean field coupling. We consider a large class of self consistent transfer operators and prove general statements about existence of invariant measures, speed of convergence to equilibrium, statistical stability and linear response. While most of the results presented in the paper are valid in a weak coupling regime, the existence results for the invariant measures we show also hold outside the weak coupling regime. We apply the general statements to examples of different nature: coupled continuous maps, coupled expanding maps, coupled systems with additive noise, systems made of different maps coupled by a mean field interaction and other examples of self consistent transfer operators not coming from coupled maps. We also consider the problem of finding the optimal coupling between maps in order to change the statistical properties of the system in a prescribed way.

Supersolid gap soliton in a Bose-Einstein condensate and optical ring cavity coupling system.

The system of a transversely pumped Bose-Einstein condensate (BEC) coupled to a lossy ring cavity can favor a supersolid steady state. Here we find the existence of supersolid gap soliton in such a driven-dissipative system. By numerically solving the mean-field atom-cavity field coupling equations, gap solitons of a few different families have been identified. Their dynamical properties, including stability, propagation, and soliton collision, are also studied. Due to the feedback atom-intracavity field interaction, these supersolid gap solitons show numerous new features compared with the usual BEC gap solitons in static optical lattices.

Collective dynamics of neural network with distance dependent field coupling

In this work, we analyse the collective dynamics of Hindmarsh-Rose neurons with distance dependent memristor and mean field coupling, realised by power law exponent. The memristor characterises the electromagnetic field induced by the magnetic flux. The mean field represents the global effect in the neurons which are usually influenced by enormous number of neighbours. The uniform global mean field drives the memristive neural network from Amplitude Death to synchronised bursting state. Desynchronised, Mixed Oscillatory, imperfect and complete synchronised states are attained by the network due to the interplay between memristor and uniform mean field coupling. The synchronisation scenario has been analysed in distance dependent memristive and mean field network, by varying the values of power law exponent. The distance dependent mean field coupling induces chimera and multichimera states in the system. The strength of incoherence and discontinuity measure are calculated to distinguish incoherent, chimera, multichimera and coherent states. Coherent states are unattainable for high values of power law exponent. The existence of chimera states in system with long range interactions are verified by parameter space. This work may give better understanding about the different aspects of synchronisation involved in neural networks with distance dependent coupling and proves that the non local synaptic coupling is not a prerequisite to realise chimera states.

Interfacial Entropy Profile in the One-loop Approximation

The near-critical interfacial entropy profile is calculated in the one-loop approximation of renormalized field theory. The shape of the profile is broadened by fluctuations and goes beyond the mean-field coupling between the entropy and the order parameter. The excess interfacial entropy and heat capacity are calculated by using the entropy profile. The interface creates corrections to the heat capacity and entropy of order χ/L, where $\xi$ is the correlation length, and L is a characteristic length of the system. These results are discussed in relation to finite-size scaling, surface critical phenomena, and the results of experiments and simulations.

Ageing transitions in a network of Rulkov neurons

The phenomenon of ageing transitions (AT) in a Erdős–Rényi network of coupled Rulkov neurons is studied with respect to parameters modelling network connectivity, coupling strength and the fractional ratio of inactive neurons in the network. A general mean field coupling is proposed to model the neuronal interactions. A standard order parameter is defined for quantifying the network dynamics. Investigations are undertaken for both the noise free network as well as stochastic networks, where the interneuronal coupling strength is assumed to be superimposed with additive noise. The existence of both smooth and explosive AT are observed in the parameter space for both the noise free and the stochastic networks. The effects of noise on AT are investigated and are found to play a constructive role in mitigating the effects of inactive neurons and reducing the parameter regime in which explosive AT is observed.

Infinite randomness with continuously varying critical exponents in the random XYZ spin chain

We study the antiferromagnetic XYZ spin chain with quenched bond randomness, focusing on a critical line between localized Ising magnetic phases. A previous calculation using the spectrum-bifurcation renormalization group, and assuming marginal many-body localization, proposed that critical indices vary continuously. In this work we solve the low-energy physics using an unbiased numerically exact tensor network method named the "rigorous renormalization group." We find a line of fixed points consistent with infinite-randomness phenomenology, with indeed continuously varying critical exponents for average spin correlations. A self-consistent Hartree-Fock-type treatment of the $z$ couplings as interactions added to the free-fermion random XY model captures much of the important physics including the varying exponents; we provide an understanding of this as a result of local correlation induced between the mean-field couplings. We solve the problem of the locally-correlated XY spin chain with arbitrary degree of correlation and provide analytical strong-disorder renormalization group proofs of continuously varying exponents based on an associated classical random walk problem. This is also an example of a line of fixed points with continuously varying exponents in the equivalent disordered free-fermion chain. We argue that this line of fixed points also controls an extended region of the critical interacting XYZ spin chain.

Controlling phase synchrony in the mean field coupled Hindmarsh–Rose neurons

The phase synchronization in a network of mean field coupled Hindmarsh–Rose neurons and the control of phase synchrony by an external input has been analyzed in this work. The analysis of interspike interval, with varying coupling strength, reveals the dynamical change induced in each neuron in the network. The bursting phase lines depict that mean field coupling induces phase synchrony in excitatory mode and desynchrony in inhibitory mode. The coefficient of variability, in spatial and temporal domain, signifies the deviations in firing times of neurons, in a collective manner. The Kuramoto order parameter quantifies the intermittent and complete phase synchrony, induced by excitatory mean field coupling. The capability of external input, in the form of spikes, to control the intermittent and complete phase synchrony has been analyzed. The coefficient of variability and Kuramoto order parameter has been studied by varying the amplitude, pulse width and frequency of the input. The studies have shown that high-frequency spike input, with optimum amplitude and pulse width, has high desynchronizing ability, which is substantiated by the parameter space analysis. The control of synchrony in the network of neurons may find application in rectifying neural disorders.