Synchronization Regime Research Articles

Nonlinear regimes of electric convection of poorly conducting fluids in weightlessness at low frequencies of an electric field

Electrothermal convection in a poorly conducting fluid in an alternating electric field of a horizontal capacitor is studied. The nonlinear regimes of electric convection in weightlessness are studies at low frequencies of the electric field on the basis of the pentamodal model within the framework of the electroconductive charge formation mechanism. Hysteresis transitions between two different synchronous and subharmonic regimes are found to exist. Transitions to chaos occur by means of either interemittance or a subharmonic cascade.

Light-driven synchronization of optogenetic clocks

Synthetic genetic oscillators can serve as internal clocks within engineered cells to program periodic expression. However, cell-to-cell variability introduces a dispersion in the characteristics of these clocks that drives the population to complete desynchronization. Here, we introduce the optorepressilator, an optically controllable genetic clock that combines the repressilator, a three-node synthetic network in E. coli, with an optogenetic module enabling to reset, delay, or advance its phase using optical inputs. We demonstrate that a population of optorepressilators can be synchronized by transient green light exposure or entrained to oscillate indefinitely by a train of short pulses, through a mechanism reminiscent of natural circadian clocks. Furthermore, we investigate the system’s response to detuned external stimuli observing multiple regimes of global synchronization. Integrating experiments and mathematical modeling, we show that the entrainment mechanism is robust and can be understood quantitatively from single cell to population level.

Light-driven synchronization of optogenetic clocks.

Synthetic genetic oscillators can serve as internal clocks within engineered cells to program periodic expression. However, cell-to-cell variability introduces a dispersion in the characteristics of these clocks that drives the population to complete desynchronization. Here, we introduce the optorepressilator, an optically controllable genetic clock that combines the repressilator, a three-node synthetic network in E. coli, with an optogenetic module enabling to reset, delay, or advance its phase using optical inputs. We demonstrate that a population of optorepressilators can be synchronized by transient green light exposure or entrained to oscillate indefinitely by a train of short pulses, through a mechanism reminiscent of natural circadian clocks. Furthermore, we investigate the system's response to detuned external stimuli observing multiple regimes of global synchronization. Integrating experiments and mathematical modeling, we show that the entrainment mechanism is robust and can be understood quantitatively from single cell to population level.

Continuous Space-Time Crystal State Driven by Nonreciprocal Optical Forces.

We show that the continuous time crystal state can arise in an ensemble of linear oscillators from nonconservative coupling via optical radiation pressure forces. This new mechanism comprehensively explains observations of the time crystal state in an array of nanowires illuminated with light [T. Liu et al., Nat. Phys. 19, 986 (2023).NPAHAX1745-247310.1038/s41567-023-02023-5]. Being fundamentally different from regimes of nonlinear synchronization, it has relevance to a wide range of interacting many-body systems, including in the realms of chemistry, biology, weather, and nanoscale matter.

Two-cluster synchronization in a fully coupled network of Mackey–Glass generators

We study a fully connected network of Mackey–Glass generators, each described by the Mackey–Glass delay differential equation. This system can exhibit non-trivial behaviour over time. One interesting scenario of such behaviour is cluster synchronization—regimes in which all components are divided into several groups, each oscillating in the same mode. Cluster synchronization can appear in various systems, such as neural networks and biological systems. In this work, we investigate the case of two-cluster synchronization and prove the existence of such modes.

Режимы обобщенной синхронизации грубых генераторов широкополосного сигнала при наличии частотных помех в канале связи

Possibility of the onset of generalized synchronization regimes and these applications for communication in the unidirectionally coupled wide-band generators in a presence of a frequency distortion in a communication channel is studied. There are considered three options of these generators: 1) with a robust hyperbolic chaotic attractor; 2) with a non-robust non-hyperbolic chaotic attractor; 3) with a robust strange non-chaotic attractor. Results are provided for three significant cases of frequency distortion: 1) removals in the high-frequency range; 2) removals in the low-frequency range; 3) frequency removals in the neighborhood of the main carrier frequency. Advantages of the hyperbolic and the strange non-chaotic signals for data transmission are demonstrated.

A Hamiltonian for 1/1 rotational secondary resonances, and application to small satellites of Saturn and Jupiter

In this work, we study the dynamics of rotation of the small satellites Methone and Aegaeon and revisit previous works on the rotation of Prometheus, Metis, and Amalthea. In all cases, the surfaces of section computed with the standard spin–orbit model reveal that the synchronous regime with small amplitude of libration shares another large domain in the phase space. We reproduce and apply the hamiltonian theory given in Wisdom 2004 [1] to analytically characterize the detected structure as being a secondary resonance where the period of the physical libration is similar to the orbital period of the satellite. We also show that the amplitude of libration in the secondary resonance is always larger than in the case of the other mode. Since the current rotational states of these sorts of satellites should be synchronous, our results can be considered in evolutionary studies of their rotation.

Multiscale Approach for Tuning Communication among Chemical Oscillators Confined in Biomimetic Microcompartments.

ConspectusInspired by the biological world, new cross-border disciplines and technologies have emerged. Relevant examples include systems chemistry, which offers a bottom-up approach toward chemical complexity, and bio/chemical information and communication technology (bio/chemical ICT), which explores the conditions for propagating signals among individual microreactors separated by selectively permeable membranes. To fabricate specific arrays of microreactors, microfluidics has been demonstrated as an excellent method. In particular, droplet-based microfluidics is a powerful tool for encapsulating biological entities and chemical reagents in artificial microenvironments, mostly water-in-oil microdroplets. In these systems, the interfaces are liquid-liquid, and their physicochemical properties are key factors for tuning the coupling between molecular diffusion. Simple and double emulsions, where aqueous domains are in equilibrium with oil domains through boundary layers of amphiphilic molecules, are organized assemblies with high interfacial-area-to-volume ratios. These membranes can be engineered to obtain different surface charges, single- or multilayer stacking, and a variable degree of defects in molecular packing. Emulsions find application in many fields, including the food industry, pharmaceutics, and cosmetics. Furthermore, micro- and nanoemulsions can be used to model the propagation of chemical species through long distances, which is not only vital for cell signaling but also significant in molecular computing. Here we present in-depth research on the faceted world of solutions confined in restricted environments. In particular, we focused on the multiscale aspects of structure and dynamics from molecular to micro and macro levels. The Belousov-Zhabotinsky chemical reaction, known for its robustness and well-documented oscillatory behavior, was selected to represent a generic signal emitter/receiver confined within microenvironments separated by liquid-liquid interfaces. In this pulse generator, the temporal and spatial progressions are governed by periodic fluctuations in the concentration of chemical species, which act as activatory or inhibitory messengers over long distances. When organized into "colonies" or arrays, these micro-oscillators exhibit emergent dynamical behaviors at the population level. These behaviors can be finely tuned by manipulating the geometrical distribution of the oscillators and the properties of the interfaces at the nanoscale. By carefully selecting the membrane composition, it is possible to drive the system toward either in-phase, antiphase, or mixed synchronization regimes among individual oscillators, depending on messenger molecules. This relatively simple lab-scale model replicates some of the communication strategies commonly found in biological systems, particularly those based on the passive diffusion of chemical and electrical signals. It can help shed light on fundamental life processes and inspire new implementations in molecular computing and smart materials.

Intermittent generalized synchronization and modified system approach: Discrete maps.

The present work deals with the intermittent generalized synchronization regime observed near the boundary of generalized synchronization. The intermittent behavior is considered in the context of two observable phenomena, namely, (i) the birth of the asynchronous stages of motion from the complete synchronous state and (ii) the multistability in detection of the synchronous and asynchronous states. The mechanisms governing these phenomena are revealed and described in this paper with the help of the modified system approach for unidirectionally coupled model oscillators with discrete time.

Quantum Synchronization and Entanglement of Dissipative Qubits Coupled to a Resonator.

In a dissipative regime, we study the properties of several qubits coupled to a driven resonator in the framework of a Jaynes-Cummings model. The time evolution and the steady state of the system are numerically analyzed within the Lindblad master equation, with up to several million components. Two semi-analytical approaches, at weak and strong (semiclassical) dissipations, are developed to describe the steady state of this system and determine its validity by comparing it with the Lindblad equation results. We show that the synchronization of several qubits with the driving phase can be obtained due to their coupling to the resonator. We establish the existence of two different qubit synchronization regimes: In the first one, the semiclassical approach describes well the dynamics of qubits and, thus, their quantum features and entanglement are suppressed by dissipation and the synchronization is essentially classical. In the second one, the entangled steady state of a pair of qubits remains synchronized in the presence of dissipation and decoherence, corresponding to the regime non-existent in classical synchronization.

Buildup and synchronization regimes of a vector pure-quartic soliton molecule in a fiber laser cavity.

Pure-quartic solitons (PQSs) have recently received increasing attention due to their energy-width scaling over the traditional soliton, which has expanded our understanding of soliton dynamics with high-order dispersion in nonlinear systems. Here, we numerically reveal the asynchronization and synchronization processes of the sub-pulse within the vector PQS molecule in a mode-locked fiber laser by solving the coupled Ginzburg-Landau equations. During the establishment of a vector PQS molecule, the repulsion, attraction, and finally stabilization processes have been observed. Specifically, sub-pulse disappearance, regeneration, and finally synchronization with the other pulses are also investigated. Our analysis of the pulse energy, time interval, and relative phase evolution dynamics with the round trip indicates that the asynchronization and synchronization within the vector PQS molecule associate tightly with the gain competition and the cross-phase modulation. Our findings provide insights into the internal mutual dynamics within the vector soliton molecule and offer guidance for the applications of PQS.

A Method to Detect the Characteristics of Intermittent Generalized Synchronization Based on Calculation of Probability of the Synchronous Regime Observation

A Method to Detect the Characteristics of Intermittent Generalized Synchronization Based on Calculation of Probability of the Synchronous Regime Observation

Synchronization regimes in the ring of rodent hippocampal neurons at limbic epilepsy

This study aims to consider an ensemble of hippocampal neurons coupled in a ring, which may be responsible for generation of the primary rhythm at limbic epilepsy. Methods. Model equations were solved numerically. To determine the areas of oscillatory and excitable regime existance for a single neuron, the bifurcation analysis for the leakadge conductivity parameter was performed. The coupling delays was not implemented directly, instead, inertia in the synapse was introduced. To determine the stability of generation some couplings were removed and parameter detunig was introduced. Results. In the single neuron model the bistability region was detected, in which a stable focus coexhists with a limit cycle. Two main synchronous regimes were detected. The first regime inherits frequency of individual oscillator, with a relatively small phase shift between oscillators in the ring. The frequency of the second regime depends on the number of neurons in the ring, with the phase shift between neighbor oscillators being equal to ratio of oscillation period and number of neurons. This second regime can occur both for the parameters corresponding to bistabler regime in the individual neuron and for the parameters at which the only existing attractor is stable focus. The second synchronous regime is preserved for parameter detuning of 2% from their absolute values. Conclusion. It was shown that in the mathematical model of the ring of hippocampal neurons, where all the main significant currents are taken into account for individual neurons, and their parameters can vary, there is an oscillatory mode, the frequency of which is determined by the length of the ring and synaptic conductivity, rather than by the parameters individual neuron. In this case, a small change in synaptic conductivity can lead to a sharp (2–7 times) change in the generation frequency.

ОСОБЕННОСТИ СИНХРОНИЗАЦИИ ДИНАМИКИ ЧИСЛЕННОСТИ В СИСТЕМЕ ТРЕХ МИГРАЦИОННО СВЯЗАННЫХ ПОПУЛЯЦИЙ

The article is devoted to the study of oscillations (cycles) synchronization in a system of three populations coupled by migration in a circle. We consider a discrete time model of population dynamics, which is a system of three identical dissipatively connected logistic maps. One-dimensional bifurcation diagrams (trees) were constructed, supplemented with the capture index of the population numbers cycles phases at adjacent sites. We conducted numerical experiments that show phase multistability – the cycles coexistence with different phases. Using qualitative methods for studying dynamic systems, a complete phase portrait of the model is constructed, showing that in the phase space there are several periodic points corresponding to elements of synchronous (in-phase) and asynchronous (out-of-phase) cycles. The 2- and 3-cycle stability conditions are investigated. It is shown that these two cycles are represented by three options: 1) a fully synchronous regime, when the abundances in the three populations coincide at any point in time; 2) a partially synchronous regime, when abundances coincide only for two populations, 3) a non-synchronous (out-of-phase) regime, when all three numbers have different values. For a 2-cycle, the third regime is unstable, possible as part of a long transition process. We found that for the 3-cycle, besides to the synchronous and partially synchronous regime, it is possible a stable out-of-phase behavior of three populations. It is shown that stable and unstable periodic points lie on certain surfaces (invariant manifolds), which separate the areas of attraction for regimes with different degrees of phase synchronization.

Intermittent behavior near the boundary of generalized synchronization in unidirectionally coupled time-delayed systems

The aim of the work is an analysis of characteristics of intermittent behavior taking place near the boundary of generalized synchronization in unidirectionally coupled time-delayed generators. The case of interaction of systems characterized by different numbers of positive Lyapunov exponents is considered. To determine the lengths of characteristic phases of the system behavior the auxiliary system method has been used. The result of the work is the determination of the type of intermittency taking place near the boundary of generalized synchronization. In this case by calculation the statistical characteristics of the laminar phase lengths (distributions of the laminar phase lengths and the dependencies of the mean lengths of the laminar phases on the criticality parameters) it has been found that near the boundary of the synchronous regime the on-off intermittency is observed. It has been shown that the intermittent generalized synchronization in time-delayed systems is characterized by multistability. For these purposes a time-averaged measure of multistability depending on the value of the coupling parameter between systems has been calculated and compared with the behavior of the spectrum of Lyapunov exponents. It has been found that the multistability measure can be used to detect the generalized synchronization in time-delayed systems.

Passive control of flow-induced vibration of a sphere using a trip wire

We experimentally investigated the potential of a trip wire as a passive control mechanism for controlling flow-induced vibration (FIV) of a three-dimensional bluff body. The effect of a surface trip wire was investigated for varying diameter ratio in the range 1.3×10−2⩽k/D⩽6.7×10−2, where k is the wire diameter and D is the sphere diameter, and trip-wire location in the range 20∘≤ϕ≤60∘, where the angle ϕ was measured from the leading stagnation point. The FIV response of the sphere is characterised for a wide range of reduced velocities 3⩽U∗⩽20, defined as U∗=U/fnwD, where U is the free stream velocity and fnw is the natural frequency of the system in water. It was found that for a fixed trip-wire diameter ratio, the vibration amplitude decreased progressively with increasing ϕ. Furthermore, the synchronisation regime became narrower, and the mode II and the plateau branches of the FIV response occurred for lower reduced velocities, compared to those for a smooth sphere. The control was highly effective for high reduced velocities (U∗>10) with a maximum reduction of up to 97.8% for ϕ=60∘. Interestingly, thicker trip wires (k/D>1.3×10−2) were effective in disrupting Mode I, but induced a galloping-like response for higher reduced velocities. Tripping proved to be an effective passive control strategy for spheres, with the optimal trip-wire size varying across Mode I to Mode III.

Synchronization, Desynchronization, and Intermediate Regime of Breathing Solitons and Soliton Molecules in a Laser Cavity.

We report on the experimental and numerical observations of synchronization and desynchronization of bound states of multiple breathing solitons (breathing soliton molecules) in an ultrafast fiber laser. In the desynchronization regime, although the breather molecules as wholes are not synchronized to the cavity, the individual breathers within a molecule are synchronized to each other with a delay (lag synchronization). An intermediate regime between the synchronization and desynchronization phases is also observed, featuring self-modulation of the synchronized state. This regime may also occur in other systems displaying synchronization. Breathing soliton molecules in a laser cavity open new avenues for the study of nonlinear synchronization dynamics.

Synchronisation of the ensemble of nonidentical FitzHugh–Nagumo oscillators with memristive couplings

The aim of the study is to investigate the features of synchronization in ensembles of nonidentical neuron-like FitzHugh–Nagumo oscillators interacting via memristor-based coupling. Methods. The collective dynamics in a ring of FitzHugh–Nagumo oscillators connected via memristive coupling was studied numerically and experimentally. The nonidentity of oscillators was achieved by detuning them by the threshold parameter responsible for the excitation of oscillator, or by detuning them by the parameter characterizing the ratio of time scales, the value of which determines the natural frequency of oscillator. We investigated the synchronization of memristively coupled FitzHugh–Nagumo oscillators as a function of the magnitude of the coupling coefficient, the initial conditions of all variables, and the number of oscillators in the ensemble. As a measure of synchronization, we used a coefficient characterizing the closeness of oscillator trajectories. Results. It is shown that with memristive coupling of FitzHugh–Nagumo oscillators, their synchronization depends not only on the magnitude of the coupling coefficient, but also on the initial states of both the oscillators themselves and the variables responsible for the memristive coupling. We compared the synchronization features of nonidentical FitzHugh–Nagumo oscillators with memristive and diffusive couplings. It is shown that, in contrast to the case of diffusive coupling of oscillators, in the case of meristive coupling, with increasing coupling strength of the oscillators, the destruction of the regime of completely synchronous in-phase oscillations can be observed, instead of which a regime of out-of-phase oscillations appears. Conclusion. The obtained results can be used when solving the problems of synchronization control in ensembles of neuronlike oscillators, in particular, for achieving or destroying the regime of in-phase synchronization of oscillations in an ensemble of coupled oscillators.

The Interplay of Common Noise and Finite Pulses on Biological Neurons

The response of neurons is highly sensitive to the stimulus. The stimulus can be associated with a direct injection in vitro experimentation (e.g., time dependent and independent inputs); or post-synaptic potentials resulting from the interaction of many neurons. A typical incoming stimulus resembles a noise which in principle can be described as a random variable. In computational neuroscience, the noise has been extensively studied for different setups. In this study, we investigate the effect of noisy inputs in a minimal network of two identical leaky integrate-and-fire (LIF) neurons interacting with finite pulses. In particular, we consider a Gaussian white noise as a standard function for stochastic modelling of neurons, while taking into account the pulse width as an elementary component for the signal transmission. By exploring the role of noise and finite pulses, the two neurons show a synchronous spiking behaviour characterized by fluctuations in the interspike intervals. Above some critical values the synchronous regime collapses onto asynchronous dynamics. The abrupt change in such dynamics is accompanied by a hysteresis, i.e., the coexistence of synchronous and asynchronous firing behaviour.

Extreme synchronization events in a model neuron-astrocyte network

The examination of synchronization in neural networks is essential to comprehend how the brain functions in normal and pathological states. The synchronization of signals between groups of neurons is paramount for brain activity and associated with various brain functions, including memory, movement, sleep, and attention. However, a balance between synchronization and desynchronization must be maintained for proper brain function. During epilepsy, spontaneous transitions occur between two states of brain activity: synchronous and asynchronous. These transitions can be induced by various factors, including imbalances in chemical signals, changes in network activity, and other mechanisms that are not yet fully understood. Understanding these spontaneous transitions and the underlying mechanisms is a crucial aspect of epilepsy research. It will lead to the development of novel treatment approaches and strategies for inhibiting synchronized activity and averting seizure episodes. A neuron-astrocyte network model was constructed in this study, which displayed spontaneous and induced transitions between asynchronous and synchronous states triggered by external stimuli. The network model utilized 1000 Izhikevich neurons [1] interconnected with excitatory synapses and organized according to a scale-free graph. Each neuron had a bidirectional interaction with a single astrocyte, resulting in a total of 1000 astrocytes in the network. The Ullah model [2] simulated intracellular calcium ion concentration dynamics in a single astrocyte. The action potential generated by a neuron causes the release of neurotransmitters into the synaptic cleft, which triggers the corresponding astrocyte to release calcium ions from its endoplasmic reticulum into the cytoplasm, generating a calcium impulse. The calcium pulse within the astrocyte led to the release of a gliotransmitter. This gliotransmitter has the potential to regulate the synaptic transmission efficiency of both presynaptic and postsynaptic terminals associated with the respective astrocyte. The study simulated the effect of astrocytic suppression on neurotransmitter release. The strength of the synaptic input connection to the neuron that interacts with the astrocyte decreased in proportion to the amplitude of the calcium pulse in the astrocyte. Within the context of the implemented model study, we analyzed the global order parameter’s dependence on the maximum synaptic weight. Our bifurcation analysis showed the presence of hysteresis within a specific range of parameter values for connection weight maximums. In this range, the system under consideration is capable of displaying both synchronous and asynchronous regimes. However, an asynchronous regime was the only observed outcome below the lower boundary of the range, and only a synchronous regime was observed above the upper boundary. A statistical analysis was carried out on the duration of the model’s asynchronous states, specifically for the parameter value of the maximum synaptic weight near the upper boundary of the hysteresis region. The network dynamics were simulated for a prolonged period, and a histogram of the asynchronous state durations was plotted on a double logarithmic scale. The resulting data points were approximated using linear regression, which yielded a power-law exponent of –3/2. Based on the obtained results, the neuron-astrocyte network can exhibit spontaneous transitions between two states: synchronous and asynchronous, similar to pathological processes in the brain. More precisely, the power-law exponent of –3/2 aligns with values discovered in experimental recordings of epileptic activity in rodent brains [3–5]. Detailed modeling of biophysical processes revealed the spontaneous emergence of global order in the network induced by noise. Astrocytic effects mediated the disruption of synchronization in the neural network by reducing the efficiency of synaptic transmission.