Synchronization analysis of complex networks of nonlinear oscillators. Stochastic synchronization of genetic oscillator networks. Bidirectional synchronization of two identical jerk circuit synchronization between the master and slave systems is said to be achieved if et o 0 as to f. Introduction this paper addresses the synchronization of identical oscillators connectedthrougha networkrepresentedby a dynamical. Theme coupled oscillators provide a useful paradigm for the study of collective behavior of large complex systems a wonderful world to be in full of interesting mathematical challenges and novel applications physics, chemistry, biology, economics. Synchronization analysis of coupled noncoherent oscillators. Example of coupling function and synchronization 6. Adaptive synchronization strategies in a network of nonlinear oscillators have been a topic of much interest e. Oscillators with frequency mismatch, as well as with nonidentical excitation parameters which determine the oscillation amplitudes, are considered.
Experimental investigation of highquality synchronization. A design principle for minimizing the influence of noise is also presented. For example, a phase distribution with r2 0 and r1. Experimental huygens synchronization of oscillators. Bullo ucsb sync in complex oscillator networks cdc 2012 5 37 phenomenology and challenges in synchronization synchronization is a tradeo. Synchronization of noncoherent oscillators 7 27100 27150 27200 27250 27300 27350 time 0 10 20 y d 1 y d, t d 2 t d 2 6 10. A return map analysis gives us a systematic analysis of stabilities of the 1. Synchronization of indirectly coupled lorenz oscillators.
Understanding the molecular mechanisms that are responsible for oscillations and their collective behaviors is important for clarifying the dynamics of cellular life and for designing efficient drug doses. Synchronization of coupled mechanical oscillators 115 figure 3 bifurcation diagram of three coupled dung oscillators 5. A model study abhinav parihar,1, a nikhil shukla,2, b suman datta,2, c and arijit raychowdhury1, d. Phase synchronization ps in coupled chaotic oscillators has been investigated numerically in lorenz, rossler models and also experimentally in cardiorespiratory systems by many researchers. Lag synchronization ls is an intermediate step between complete cs. From the stability criteria of the msf, we construct optimal networks with. To meet this objective it was decided to design an electromechanical setup in such a way that its mechanical counterpart is capable to model. For example, three identical oscillators coupled in a ring can be phaselocked.
In this paper, the stochastic synchronization of timecoupled nonidentical genetic networks is investigated. The observed frequency in the ensemble of coupled funnel attractors with parameters of. Coupled oscillators and biological synchronization a subtle mathematical thread connects clocks, ambling elephants. Synchronization of pairwisecoupled, identical, relaxation. We study a system of n 1 phase oscillators placed on a circle with random initial positions and sinusoidal coupling with their k nearest neighbors on each side. Moving toward a mechanical realization of the kuramoto model linda lee kennedycolumbus public schools dr. Cheng, synchronization of coupled discretetime harmonic oscillators with rational frequency, institute of electrical and electronics. The oscillators are assumed to be coupled by diffusion gradients.
Such non identical if oscillators typically interact with each other via excitatory or inhibitory synaptic stimuli. Global synchronization of delaycoupled genetic oscillators. Synchronization of oscillators manifests itself in many natural phenomena, partly because of the broad interpretation of the words oscillator and synchrony. Let xi be the mdimensional vector of dynamical variables of the ith node. Synchrony and pattern formation of coupled genetic oscillators on a. Synchronization ability of coupled cellcycle oscillators.
Chemical oscillators with a broad frequency distribution are photochemically coupled in network topologies. Adaptive synchronization of coupled chaotic oscillators. The extension of the master stability function msf to analyse stability of generalized synchronization for coupled nearly identical oscillators is discussed. Stuartlandau oscillators interconnected by linear coupling. Here, we demonstrate the synchronization of two dissimilar micromechanical oscillators using the. By exploiting the specific properties of many genetic oscillator models, we provide an easyverified sufficient condition for the stochastic synchronization of coupled genetic oscillators, based on the lure system approach in control theory. Sep 22, 2008 synchronization of genetic or cellular oscillators is a central topic in understanding the rhythmicity of living organisms at both molecular and cellular levels.
Hudson3 1institute of physics, universitat potsdam,14469 potsdam, germany. For dr coupled oscillators, we consider systems where either the direction of. Synchronization of two coupled multimode oscillators with. The considered network is based on a set of oscillators. In this case, the interaction between two oscillators that are moving in synchrony is minimal. The upper panel shows the deviation from the linear.
Note that these oscillators are not chaotic but display a. A model study abhinav parihar,1,a nikhil shukla,2,b suman datta,2,c and arijit raychowdhury1,d 1school of electrical and computer engineering, georgia institute of technology, atlanta, georgia 30332, usa. Clustering has been investigated for different systems, including identical onedimensional maps, e. Anything that progresses periodically through a cycle can be called an oscillator and communication between oscillators can lead to the creation of synchronized. Synchronization of coupled harmonic oscillators using.
It occurs at di erent levels, ranging from the small scale of the cardiac pacemaker cells of the sa sinoatrial and av atriumventricular nodes in the human hearth that synchronously re and give the pace. Collective cell movement promotes synchronization of. Unidirectional synchronization of experimental boolean phase oscillators and weakcoupling analogy by combining the phase detector from fig. As an example, we consider socalled integrateandfire dynamics. Synchronization of globally coupled nonlinear oscillators. Restoration of rhythmicity in diffusively coupled dynamical. One of the most spectacular examples of this kind of coupling can be seen along the tidal rivers of ma laysia, thailand and new guinea.
In this paper, a new synchronization problem for the collective dynamics among genetic oscillators with unbounded timevarying delay is investigated. In some situations, for example the lateral line primordium of zebrafish. They incorpo rate a dissipative mechanism to damp oscillations that grow too large and a source of energy to pump up those that become too small. Synchronization of coupled oscillator dynamics sciencedirect. The method of linear difference signal has been applied. In other words, the delaycoupled identical genetic oscillators can reach to the global exponential synchronization by regulating the connection weight matrix and the delayed connection weight matrix. In this study, we focus on the structure of synchronization picture for identical and nonidentical coupled oscillators with nonlinear timedelayed dissipative coupling 7. Adaptive synchronization of two coupled nonidentical hindmarshrose. Synchronization of oscillators universiteit utrecht.
A model study abhinav parihar,1, a nikhil shukla,2, b suman datta,2, c and arijit raychowdhury1, d 1school of electrical and computer engineering, georgia institute of technology, atlanta, georgia 30332, usa. Periodical structure of amplitude death and broadband. Synchronization of nonlinear biochemical oscillators coupled. This paper studies synchronization of identical phasecoupled oscillators with arbitrary underlying connected graph for a large class of coupling functions. Networkdriven synchronisation of phasecoupled oscillators. E 81, 046216 2010 is verified by physical experiments with electronic circuits.
Antiphase synchronization in symmetrically coupled selfoscillators 851 a b fig. Examples include synchronization 9,1719, amplitude and oscillation death 2023. In a system of coupled oscillators, synchronization occurs when oscillators spontaneously lock to a common frequency or phase. If some conditions on the magnitude of the diffusion coefficients are satisfied, it is proved that. Synchronization of coupled oscillators is a game huibing yin, prashant g. We use the bpo in the rest of the paper to study synchronization of coupled. As proposed in 32, we use a network of weakly coupled oscillators for pattern recognition. Understanding how biochemical networks lead to largescale non equilibrium. Pikovsky et al synchronization in a population of globally etc. Our main contribution is to develop the negative cut instability condition theorem 2. For all the coupled oscillators the components of lij i. Experimental huygens synchronization of oscillators 7 observe and analyze the synchronous behavior for rather di.
Two new results on exponential synchronization of delaycoupled genetic oscillators are given in section 3. Overview point of the paper model for 2 oscillators model for n oscillators main theorem conclusion synchronization of what coupled biological who. Feng june 25, 2004 abstract two coupled delayline oscillators are modeled by a system of delay di. This study provides insights for understanding the collective behaviors in many fields, such as the power grids, the flashing of fireflies, the rhythm of pacemaker cells of the heart, and even some social phenomena 1,2,3,4. For example, the onset of ad and od could seriously weaken and even. Here we analyze the stability of the synchronization of a network of oscillators coupled through different variables. We find that a core assumption of the ottantonsen ansatz is not valid in our test systems. This phenomenon occurs even if the oscillators are not identical. Inherent multistability in arrays of autoinducer coupled. Exploring synchronization in complex oscillator networks. Stewart and golubitsky showed that hopfs idea can be c ofcoupled iden tical oscillators, whose states undergo bifurcations to produce standard pat terns ofphase locking.
Oscillations play a vital role in many dynamic cellular processes, and two typical examples of genetic oscillators are the cell cycle oscillators 1,2 and circadian clocks. Indeed, synchrony is the most famil iar mode of organization for coupled oscillators. Helmut schmidt networkdriven synchronisation of phasecoupled oscillators. Synchronization phenomena in coupled nonidentical chaotic circuits ch. The breakdown of synchronization in systems of nonidentical. In this study, we focus on the structure of synchronization picture for identical and non identical coupled oscillators with nonlinear timedelayed dissipative coupling 7. Bidirectional synchronization of two identical jerk. Amplitude envelope synchronization in coupled chaotic. Existing coupled micromechanical oscillators suffer from limited range, neighborhood restriction and non congurable coupling which limit the control, physical size and possible topologies of complex oscillator networks 1,2. Cells in the psm have a genetic oscillator composed of negative feedback loops 1520. Genetic networks are intrinsically noisy due to natural random intra and intercellular fluctuations. Many biological oscillators show synchronized oscillations, not because of the presence. To study the effect of collective cell movement on the synchronization of coupled genetic oscillators, we examine the dependence of the phase order parameter z on the polarity alignment strength. This setup is useful for both educational and research purposes.
Ps and is have also been studied in unidirectionally coupled chaotic systems. The corresponding differential equations have been integrated analytically and the. Oscillators that have a standard wave form and amplitude to which they re turn after small perturbations are known as limitcycle oscillators. Sij and pij can be computed and accordingly synchronization of linearly coupled fhn oscillator can be shown.
Oscillators coupled in a network can synchronize with each other to. Synchronization of genetic or cellular oscillators is a central topic in understanding the rhythmicity of living organisms at both molecular and cellular levels. Synchronization versus neighborhood similarity in complex. A design principle underlying the synchronization of oscillations in. The study of synchronization of coupled biological oscillators is. Oscillators assume to interact by a simple form of pulse coupling when a given oscillator fires, its pulls all the other oscillators up by an amount, or pulls them up to firing. Synchronization of pulsecoupled biological oscillators. The study of coupled oscillators showed that a stable rhythm could arise from a. A mutual coupling of identical 3d jerk circuit fig. We show that this coherent behaviour is due to synchronization of phases of these oscillators, while their amplitudes remain chaotic. Synchronization of diffusively coupled oscillators.
Synchronization of pairwisecoupled, identical, relaxation oscillators based on metalinsulator phase transition devices. Coupled nonlinear oscillators roberto sassi 1 introduction mutual synchronization is a common phenomenon in biology. Even with weak coupling as huygens saw with his clocks, nonidentical oscillators can interact in such a way to synchronize to each other. Synchronization of phasecoupled oscillators with plastic. Synchronization transition in a pair of coupled non. Synchronization of phasecoupled oscillators with arbitrary.
This model is also interesting because it approximates dynamics of a large class of non linear oscillators near limit cycle, under weak mutual interaction 6. Networkdriven synchronisation of phasecoupled oscillators helmut schmidt university of exeter. The primary example has been legged locomotion that has been modeled as coupled. Ad regimes of delay coupled identical oscillators for aoamin. Phase synchronization occurs when the coupled chaotic oscillators keep their phase difference bounded while their amplitudes remain uncorrelated. Experimental evidence on intermittent lag synchronization.
Furthermore, we assume that the oscillators are nearly identical and that the. Request pdf synchronization of coupled nonidentical genetic oscillators the study of the collective dynamics of synchronization among genetic oscillators is essential for the understanding of. The dynamical behaviour of coupled oscillators with or without time delays have been studied by many researchers 123456789101112 14 1516171819. Dictyostelium cellular oscillators are coupled by cyclic adenosine. Synchronization in a population of globally coupled. In section 4, an example is provided to show the validities and properties of the synchronization conditions. Motivation the classical kuramoto model networks of kuramoto models. Identical synchronization is the particular case of generalized synchronization when. Throughout this paper, r n denotes the ndimensional euclidean space.
In some cases, analytical description is provided, but only for a few simple special examples such as two connected oscillators 29. Pdf synchronized oscillations and chaos in coupled. Sorrentino and ott 10 proposed and simulated an ef. We obtain analytical boundaries for the domain of broadband synchronization and investigate transition mechanisms between different synchronization modes. Synchronization of coupled nonidentical genetic oscillators.
Here, we show how a collective rhythm across a population of genetic oscillators through synchronization induced intercellular communication is achieved, and how an ensemble of independent genetic oscillators is synchronized. Coupled oscillators and biological synchronization request pdf. Therefore, it is important to study the effects of noise perturbation on the synchronous dynamics of genetic oscillators. Morelli2, 1theoretical biology laboratory, riken, 21 hirosawa, wako, saitama, japan. The nearly identical nature of the coupled oscillators is due to some parameter mismatch while the dynamical equations are the same for all the oscillators. Synchronization phenomena in coupled nonidentical chaotic. Synchronization of identical oscillators coupled through a. In particular, the phenomenon of complete synchronization is the most studied type of synchronization. We present the results of both, theoretical and experimental investigations of synchronization between two, three and four almost identical oscillators. Generally, a group of oscillators is said to be synchronized when each oscillators frequency has locked onto the same value as all the others 1, 810. We mimic this behavior with two wellmatched, oneway coupled nonlinear rc circuits driven by identical sinusoidal signals.
Synchronization processes in populations of identical networked oscillators are the focus of intense studies in physical, biological, technological, and social systems. Identical oscillators network as nonlinear consensus. Synchronization in dynamical systems of coupled oscillators is one important issue in the frontier of nonlinear dynamics and complex systems. The study of synchronization among genetic oscillators is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. Synchronization phenomena for coupled delayline oscillators. A new concept called powerrate synchronization, which is different from both the. May 20, 2015 in this paper, a new synchronization problem for the collective dynamics among genetic oscillators with unbounded timevarying delay is investigated. The dynamical system under consideration consists of an array of linearly coupled identical genetic oscillators with each oscillators having unbounded timedelays. Synchronization stability in coupled oscillator arrays 275 theory in the context of lyapunov exponents as a stability criterion and show in the conclusions how the other criteria can be used.
Synchronization of kuramoto oscillators with nonidentical. In a system of coupled oscillators, synchronization occurs when the oscillators spontaneously lock to a common frequency or phase. Shanbhag abstractthe purpose of this paper is to understand phase transition in noncooperative dynamic games with a large number of agents. Here, we show how a collective rhythm across a population of genetic oscillators through synchronization induced intercellular communication is achieved, and how an ensemble of independent genetic oscillators is synchronized by a. Synchronization in a population of globally coupled chaotic. Collective cell movement promotes synchronization of coupled. Phaselag synchronization in networks of coupled chemical. The breakdown of synchronization in systems of non identical chaotic oscillators. Stochastic synchronization of genetic oscillator networks bmc. We demonstrate synchronization transition in a large ensemble of nonidentical chaotic oscillators, globally coupled via the mean. Synchronization of coupled optomechanical oscillators. Synchronization of kuramoto oscillators with nonidentical natural frequencies.
The inphase and antiphase synchronization of indirectly coupled chaotic oscillators reported in phys. Experiments and simulations show that the network synchronization occurs by phaselag. Synchronization phenomena for coupled delayline oscillators carmen chicone. It is a suf cient condition for an equilibrium to be unstable. This paper studies synchronization of identical phase coupled oscillators with arbitrary underlying connected graph for a large class of coupling functions. Ad regimes of delaycoupled identical oscillators for aoamin. We do not consider cell division and cell apoptosis in the theory for simplicity. A classic example of distributed coordination in physics, engineering and biology is the synchronization of arrays of coupled nonlinear oscillators 15, 16, 25. Macroscopic models for networks of coupled biological oscillators. Synchronizationoptimized networks for coupled nearly. In this paper complete synchronization of diffusively coupled oscillators is considered.
In addition, these conditions are dependent on both the connection weight matrix and the delayed connection weight matrix. Synchronization of coupled boolean phase oscillators. Exeter, 4th feb 2014 helmut schmidt networkdriven synchronisation of phasecoupled oscillators. Synchronization of coupled oscillator dynamics request pdf. Moreover, those works that study systems of phase coupled oscillators with plastic coupling strengths generally contain only empirical insights and interesting simulation results. A new concept called powerrate synchronization, which is different from both. Network dynamics of coupled oscillators and phase reduction. Spontaneous chaos synchronization, and its practical applications in communication,, optics, biology and ecology have been an active subject of curiosity and scholar inquiry for many years, especially since the work of pecora and carroll in 1990, where it was shown that when a state variable from a chaotic system is input into a replica subsystem of the original. Index terms synchronization, coupled oscillators, lti network, voltage power supplies. Ren, synchronization of coupled harmonic oscillators with local interaction, automatica, vol. Article collective cell movement promotes synchronization of coupled genetic oscillators koichiro uriu1, and luis g. Index termssynchronization, coupled oscillators, lti network, voltage power supplies.
550 565 1185 1478 301 737 623 879 1511 114 768 238 958 1168 1352 155 1211 289 1255 962 1443 381 1335 425 98 444 1037 1272 1347 444 388