Antiphase States Research Articles

In-plane charged antiphase boundary and 180° domain wall in a ferroelectric film

The deterministic creation and modification of domain walls in ferroelectric films have attracted broad interest due to their unprecedented potential as the active element in non-volatile memory, logic computation and energy-harvesting technologies. However, the correlation between charged and antiphase states, and their hybridization into a single domain wall still remain elusive. Here we demonstrate the facile fabrication of antiphase boundaries in BiFeO3 thin films using a He-ion implantation process. Cross-sectional electron microscopy, spectroscopy and piezoresponse force measurement reveal the creation of a continuous in-plane charged antiphase boundaries around the implanted depth and a variety of atomic bonding configurations at the antiphase interface, showing the atomically sharp 180° polarization reversal across the boundary. Therefore, this work not only inspires a domain-wall fabrication strategy using He-ion implantation, which is compatible with the wafer-scale patterning, but also provides atomic-scale structural insights for its future utilization in domain-wall nanoelectronics.

Synchronization of delayed coupled neurons with multiple synaptic connections.

Synchronization is a key feature of the brain dynamics and is necessary for information transmission across brain regions and in higher brain functions like cognition, learning and memory. Experimental findings demonstrated that in cortical microcircuits there are multiple synapses between pairs of connected neurons. Synchronization of neurons in the presence of multiple synaptic connections may be relevant for optimal learning and memory, however, its effect on the dynamics of the neurons is not adequately studied. Here, we address the question that how changes in the strength of the synaptic connections and transmission delays between neurons impact synchronization in a two-neuron system with multiple synapses. To this end, we analytically and computationally investigated synchronization dynamics by considering both phase oscillator model and conductance-based Hodgkin-Huxley (HH) model. Our results show that symmetry/asymmetry of feedforward and feedback connections crucially determines stability of the phase locking of the system based on the strength of connections and delays. In both models, the two-neuron system with multiple synapses achieves in-phase synchrony in the presence of small and large delays, whereas an anti-phase synchronization state is favored for median delays. Our findings can expand the understanding of the functional role of multisynaptic contacts in neuronal synchronization and may shed light on the dynamical consequences of pathological multisynaptic connectivity in a number of brain disorders.

Energy dependence of synchronization mode transitions in the delay-coupled FitzHugh-Nagumo system driven by chaotic activity.

Energy absorption and consumption are essential for the activity of single neurons and neuronal networks. The synchronization mode transition and energy dependence in a delay-coupled FitzHugh-Nagumo (FHN) neuronal system driven by chaotic activity are investigated in this paper. With the change of chaotic current intensity, it was found that the synchronization mode of coupled neurons undergoes synchronous state, transition state, anti-phase state, alternating asynchronous and anti-phase state, and chaotic current-induced chaotic state. The Hamiltonian energy is much dependent on the synchronization mode of coupled neurons. The synchronization mode and the Hamiltonian energy of coupled neurons can be modulated by chaotic current intensity, coupling strength and time delay. The introduction of the time delay induces the system to become bistable state. Chaotic current as an external force induced transitions between the synchronous and anti-phase states. Coupling strength is an intrinsic property of the system and can change the properties of the bistable state. Furthermore, the synchronous and anti-phase states appear intermittently with the increasing of time delay. A chained neuronal network is used to prove that the synchronization mode transition of the system of multiple neurons is similar to the two neurons. The results of this paper might help one to understand the intrinsic energy alteration mechanisms of neuronal synchronization.

Extreme multistability in symmetrically coupled clocks

Extreme multistability (EM) is characterized by the emergence of infinitely many coexisting attractors or continuous families of stable states in dynamical systems. EM implies complex and hardly predictable asymptotic dynamical behavior. We analyze a model for pendulum clocks coupled by springs and suspended on an oscillating base and show how EM can be induced in this system by specifically designed coupling. First, we uncover that symmetric coupling can increase the dynamical complexity. In particular, the coexistence of multiple isolated attractors and continuous families of stable periodic states is generated in a symmetric cross-coupling scheme of four pendulums. These coexisting infinitely many states are characterized by different levels of phase synchronization between the pendulums, including anti-phase and in-phase states. Some of the states are characterized by splitting of the pendulums into groups with silent sub-threshold and oscillating behavior, respectively. The analysis of the basins of attraction further reveals the complex dependence of EM on initial conditions.

Sparse sensor-based flow estimation with spectral proper orthogonal decomposition

The application of Artificial Neural Networks (ANNs) in developing sensor-based estimators for unsteady flows has become an active area of research over the last decade. One of the challenges in this area is the selection of a low-dimensional subspace that enables the ANN to reconstruct relevant spatiotemporal dynamics in the flow, as both sparsity and interpretability are simultaneously desired. The present study demonstrates the use of a flow-estimation framework based on Long Short-Term Memory (LSTM) neural networks and the time-domain Spectral Proper Orthogonal Decomposition (SPOD) [Sieber et al., “Spectral proper orthogonal decomposition,” J. Fluid Mech. 792, 798–828 (2016)], which was proposed as an extension to the traditional POD. The two-cylinder flow selected for analysis in this study is referred to as the “flip-flop” regime for exhibiting intermittent changes in the phase alignment of the vortices shed by the two cylinders. This flow has dynamics occurring over a wide range of frequencies, and it was selected to demonstrate the usefulness of SPOD in characterizing the wake dynamics of periodic wake flows and to determine if it can provide a better subspace for training and estimation when compared to POD. It was found that a particular SPOD basis obtained with an empirically determined filter length completely separated the frequency centered phenomena present in the spectrum of the most energetic POD modes into different modes. These new SPOD modes were observed to have a direct relationship with the vortex dynamics in the flow, providing direct access to the antiphase and in-phase flow states. The LSTM neural networks estimation capacities were very similar across all the modal spaces investigated, performing well regardless of whether the frequency content of the modal space used for training and estimation was found superimposed in the spectrum of the most energetic modes (POD) or separated into different modes (SPOD). Further investigation is required to determine if this result holds for turbulent flows.

Self-synchronization and control-synchronization of dual-rotor space vibration system

Since the intrinsic characteristics of self-synchronization vibration system, the implementation of in-phase synchronization state is restricted, which leads to unsatisfactory force of dual-rotor system driven by two coaxial motors in the space. Thus, control synchronization is proposed in this paper to address the problems above. Firstly, to explore the defects of the self-synchronization vibration system, dynamic model of the dual-rotor space vibration system is established, and the self-synchronization mechanism of two eccentric rotors (ERs) is analyzed by small parameter average method. Subsequently, to implement the in-phase synchronization between the two ERs, controllers based on master–slave control structure (MSCS) and sliding mode control (SMC) algorithm are systematically designed. Finally, the effectiveness of self-synchronization mechanism and control-synchronization method is validated by simulations in Matlab/Simulink. The results show that the anti-phase synchronization state is appeared on account of small horizontal distance or larger installation height of the two ERs; however, with the application of controllers, the phase difference (PD) of the two ERs is successfully controlled at zero, and the strong robustness of the controllers is further demonstrated by the variations of rotation velocity and structural parameter.

Bifurcation analysis of multistability of synchronous states in the system of two delay-coupled oscillators.

Systems of mutually coupled oscillators with delay coupling are of great interest for various applications in electronics, laser physics, biophysics, etc. Time delay usually originates from the finite speed of propagation of the coupling signal. In this paper, we present the results of detailed bifurcation analysis of two delay-coupled limit-cycle (Landau-Stuart) oscillators. First, we study the simplified case when the delay time is much smaller than the oscillation build-up time. When the coupling signal propagates between the two counterparts, it acquires a phase shift, which strongly affects the synchronization pattern. Depending on this phase shift, the system may demonstrate the behavior typical for either dissipative or conservative (reactive) coupling. We examine stability of the in-phase and anti-phase synchronous states and reveal the complicated pattern of the synchronization domains on the frequency mismatch-coupling strength parameter plane paying a special attention to the mechanisms of appearance and disappearance of the phase multistability. We demonstrate that taking into account reactive phase nonlinearity the coupling signal acquires an additional phase shift, which depends on the signal intensity. We also examine the more complicated case of finite delay time. The increase of the reactive nonlinearity parameter and the delay time leads to transformations of synchronization domains similar to those that occur when the phase shift increases. For the bifurcation analysis, we employ XPPAUT and DDEBifTool package and verify the results by direct numerical integration.

Bistabilities in two parallel Kármán wakes

Bistabilities of two equilibrium states discovered in the coupled side-by-side Kármán wakes are investigated through Floquet analysis and direct numerical simulation (DNS) with different initial conditions over a range of gap-to-diameter ratio ( $g^*= 0.2\text {--}3.5$ ) and Reynolds number ( $Re = 47\text {--}100$ ). Two bistabilities are found in the transitional $g^*-Re$ regions from in-phase (IP) to anti-phase (AP) vortex shedding states. By initialising the flow in DNS with zero initial conditions, the flow in the first bistable region (i.e. bistable IP/FF $_C$ at $g^*= 1.4 \text {--} 2.0$ , where FF $_C$ denotes the conditional flip-flop flow) attains flip-flop (FF) flow, it settles into the IP state by initialising the flow with an IP flow. The second bistability is observed between cylinder-scale IP and AP states at large $g^*$ ( $=$ 2.0–3.5). The transition from the FF $_C$ to IP is dependent on initial conditions and irreversible over the parameter space, meaning that the flow cannot revert back to the FF $_C$ state once it jumps to the IP state irrespective of the direction of $Re$ variations. Its counterpart for the bistable IP/AP state is reversible. We also found that the FF $_C$ flow in the first bistable region is primarily bifurcated from synchronised AP with cluster-scale features, possibly because the cluster-scale AP flow is inherently unstable to FF flow instabilities. It is demonstrated that the irreversible bistability exists in other interacting wakes around multiple cylinders. A good understanding of flow bistabilities is pivotal to flow control applications and the interpretation of desynchronised flow features observed at high $Re$ values.

Dynamics of coupled Kuramoto oscillators with distributed delays.

This paper studies the effects of two different types of distributed-delay coupling in the system of two mutually coupled Kuramoto oscillators: one where the delay distribution is considered inside the coupling function and the other where the distribution enters outside the coupling function. In both cases, the existence and stability of phase-locked solutions is analyzed for uniform and gamma distribution kernels. The results show that while having the distribution inside the coupling function only changes parameter regions where phase-locked solutions exist, when the distribution is taken outside the coupling function, it affects both the existence, as well as stability properties of in- and anti-phase states. For both distribution types, various branches of phase-locked solutions are computed, and regions of their stability are identified for uniform, weak, and strong gamma distributions.

Synchronization mode transition induced by bounded noise in multiple time-delays coupled FitzHugh–Nagumo model

ABSTRACT Noise and time-delays are ubiquitous in physical and biological systems. In this paper, the multiple time-delays coupled FitzHugh-Nagumo (FHN) models is employed to investigate the synchronization mode transition. The orbital projection method is used to study the difference of membrane potential between two FHN neurons in the phase plane, and a measure of anti-phase is defined to characterize the synchronization state of neural system. It is shown that the synchronization mode of coupled neurons is different while changing the parameters of the system. In the absence of noise, as the coupling strength increases, the firing mode of two coupled neurons undergoes a succession of transitions (i.e., from the asynchronous state, to the completely synchronized state, then the anti-phase state, and finally to the completely synchronized state again). In the presence of noise, the synchronization mode of neurons becomes more diversified with the increasing of noise intensity. Moreover, by changing the time-delay and coupling strength, the sensitivity of two-neuron to noise can be changed, thereby the synchronization mode transition can be adjusted.

Effect of repulsive links on frustration in attractively coupled networks.

We investigate the impact of attractive-repulsive interaction in networks of limit cycle oscillators. Mainly we focus on the design principle for generating an antiphase state between adjacent nodes in a complex network. We establish that a partial negative control throughout the branches of a spanning tree inside the positively coupled limit cycle oscillators works efficiently well in comparison with randomly chosen negative links to establish zero frustration (antiphase synchronization) in bipartite graphs. Based on the emergence of zero frustration, we develop a universal 0-π rule to understand the antiphase synchronization in a bipartite graph. Further, this rule is used to construct a nonbipartite graph for a given nonzero frustrated value. We finally show the generality of 0-π rule by implementing it in arbitrary undirected nonbipartite graphs of attractive-repulsively coupled limit cycle oscillators and successfully calculate the nonzero frustration value, which matches with numerical data. The validation of the rule is checked through the bifurcation analysis of small networks. Our work may unveil the underlying mechanism of several synchronization phenomena that exist in a network of oscillators having a mixed type of coupling.

Antiphase synchronization and central symmetrical antiphase synchronization in magnetic field coupled circuits

The dynamics of memristor-based RLC circuit is explored on the effects of magnetic field coupling through a transformer in the circuit. With the increasing strength of magnetic field coupling, the two coupled RLC circuits firstly break the reflectional symmetry by transiting from double-scroll attractors to single-scroll attractors and then break the translational symmetry with two attractors in different sizes and shapes. The two single-scroll attractors are locked in antiphase synchronous states for positive magnetic field coupling while transit to a new kind of dynamic regime, named as central symmetrical antiphase synchronization (CSAS) for negative magnetic field coupling. Moreover, the single-scroll attractors in inphase synchronization or in CSAS may coexist with asynchronous states in some interval of coupling strength. The dynamics of the anti-synchronization and the CSAS of the coupled memristor-based circuits have potential applications in nonvolatile memories, neuromorphic devices to simulate learning, adaptive and spontaneous behaviors.

Phase synchronization and mode transition induced by multiple time delays and noises in coupled FitzHugh–Nagumo model

Noise and time delay are ubiquitous in various physical and biological systems. In this paper, we studied the phase synchronization and mode transition of oscillation mode induced by time delays and noises in a coupled FitzHugh–Nagumo (FHN) neural system. In the case of coupled neurons with single time delay, it is found that the mode oscillation of neurons induced by the noise and time delay undergoes a successive transitions from the synchronization, the out-of phase, the alternating phase-drift and anti-phase state, to the anti-phase state. In the case of coupled neurons with two time delays, when the two delays are comparable, the large amplitude oscillation of potential is in alternating synchronous and asynchronous state in the absence of noises, and the small amplitude oscillation of potential is always synchronized. The oscillation behaviors of coupled neurons with two time delays are similar to the cases with a single time delay in the presence of noises. When one of two time delays is largely dominant over the other, the neurons show completely different dynamic behaviors.

Neuronal communication: Stochastic neuron dynamics and multi-synchrony states

We study stochastic theory of single neuron dynamics and coherence in the cross-talk of coupled stochastic neurons. The unstable periodic orbits embedded in chaotic orbit can be unlocked by internal noise by taming the chaotic dynamics. Internal noise driven single neuron dynamics exhibit a new class of crises, which we call noise-induced crises. The cross-talk between two neurons coupled through internal noise and synaptic (memristor) coupling can trigger multi-synchrony states separated by flipping desynchronized states within a certain range of noise, which are observed in few experiments as coherent neuronal patterns. Further, transition between in-phase to anti-phase synchrony states can also be observed, driven by internal noise as well as coupling constant.

Phase-flip in relay oscillators via linear augmentation

In time-delay coupled relay system of three limit cycle of oscillators, linear augmentation control provides an effective strategy to induce phase-flip from relative phase zero to π between spatially separated oscillators. A coexisting dynamical regime of fixed point and anti-phase synchronization state is harnessed in relay system. Targeting phase-flip transition through linear augmentation is illustrated by using Stuart-Landau oscillators. However, such dynamical transition does not occur in the same system with conjugate coupling through dissimilar variables. Inducing relative phase difference without resorting to variation of internal system parameters and time-delay is important from the view of system control.

Chimera states in a bipartite network of phase oscillators

The chimera state, exhibiting a hybrid state of coexisting coherent and incoherent behaviors, has become a fast growing field in the past decade. In this paper, we investigate bipartite networks of nonlocally coupled phase oscillators. We report different types of chimera states such as in-phase chimera states, anti-phase chimera states, and syn-desyn chimera states. Phase diagrams on different parameter planes are presented.

Emergent central pattern generator behavior in chemical coupled two-compartment models with time delay

This paper proposes that modified two-compartment Pinsky–Rinzel (PR) neural model can be used to develop the simple form of central pattern generator (CPG). The CPG is called as ‘half-central oscillator’, which constructed by two inhibitory chemical coupled PR neurons with time delay. Some key properties of PR neural model related to CPG are studied and proved to meet the requirements of CPG. Using the simple CPG network, we first study the relationship between rhythmical output and key factors, including ambient noise, sensory feedback signals, morphological character of single neuron as well as the coupling delay time. We demonstrate that, appropriate intensity noise can enhance synchronization between two coupled neurons. Different output rhythm of CPG network can be entrained by sensory feedback signals. We also show that the morphology of single neuron has strong effect on the output rhythm. The phase synchronization indexes decrease with the increase of morphology parameter’s difference. Through adjusting coupled delay time, we can get absolutely phase synchronization and antiphase state of CPG. Those results of simulation show the feasibility of PR neural model as a valid CPG as well as the emergent behaviors of the particularly CPG.

Experimental observation of phase-flip transitions in two inductively coupled glow discharge plasmas.

We report an experimental observation of a phase-flip transition in the frequency synchronization of two dc glow discharge plasma sources that are coupled in a noninvasive fashion. When the fundamental oscillation frequency of the potential fluctuations of one of the sources is progressively increased, by raising its discharge voltage, a frequency pulling regime is observed, followed by a synchronized regime that shows a frequency jump phenomenon. The jump is associated with a phase-flip transition that takes the synchronized state from an in-phase to an antiphase state. When the process is reversed, the transition takes place at a different frequency, thereby exhibiting a hysteresis effect. A heuristic model, consisting of two van der Pol oscillators that are coupled to each other through a dynamic common medium, eminently captures the essential features of our experimental observations.

Interaction function of coupled bursting neurons**Project supported by the National Natural Science Foundation of China (Grant Nos. 11272065 and 11472061).

The interaction functions of electrically coupled Hindmarsh–Rose (HR) neurons for different firing patterns are investigated in this paper. By applying the phase reduction technique, the phase response curve (PRC) of the spiking neuron and burst phase response curve (BPRC) of the bursting neuron are derived. Then the interaction function of two coupled neurons can be calculated numerically according to the PRC (or BPRC) and the voltage time course of the neurons. Results show that the BPRC is more and more complicated with the increase of the spike number within a burst, and the curve of the interaction function oscillates more and more frequently with it. However, two certain things are unchanged: ϕ = 0, which corresponds to the in-phase synchronization state, is always the stable equilibrium, while the anti-phase synchronization state with ϕ = 0.5 is an unstable equilibrium.

Huygens’ Synchronization: Experiments, Modeling, and Local Stability Analysis

The synchronization of two metronomes on a freely moving platform is examined. Existence and local stability of the synchronized solutions is studied when the platform parameters are subject to change, i.e., a numerical continuation and bifurcation software tool is used to reveal local stability of the in- and/or anti-phase synchronized state as function of system parameters. It is demonstrated that the platform parameter values have a significant influence on the stability of the anti-phase synchronized solution.