Dynamical phenomena in complex networks: fundamentals and applications

Yanchuk, Serhiy; Roque, Antonio; Macau, Elbert E. N.; Kurths, Jürgen

doi:10.1140/epjs/s11734-021-00282-y

Cited by 8 publications

(7 citation statements)

References 33 publications

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“…Dynamical networks with complex topology are a very powerful approach for the study of large complex systems in various application areas ranging from neuroscience, engineering, to sociology, economics or Earth sciences. From this perspective, real-world systems are modeled as networks of interacting nodes, where the nodes have their own dynamics and influence each other's behavior in complex ways [1][2][3][4][5]. Research in this area combines various application fields with theoretical approaches from dynamical system theory, statistical physics, time series analysis, or graph theory.…”

Section: Introductionmentioning

confidence: 99%

Stabilization of synchronous equilibria in regular dynamical networks with delayed coupling

2023

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We consider the synchronization problem of dynamical networks with delayed interactions. More specifically, we focus on the stabilization of synchronous equilibria in regular networks where the degrees of all nodes are equal. By studying such control near a Hopf bifurcation, we obtain necessary and sufficient conditions for stabilization. It is shown that the stabilization domains in the parameter space reappear periodically with time-delay. We find that the frequency of reappearance of the control domains is linearly proportional to the number of cycle multipartitions of the network. IntroductionDynamical networks with complex topology are a very powerful approach for the study of large complex systems in various application areas ranging from neuroscience, engineering, to sociology, economics or Earth sciences. From this perspective, real-world systems are modeled as networks of interacting nodes, where the nodes have their own dynamics and influence each other's behavior in complex ways [1][2][3][4][5]. Research in this area combines various application fields with theoretical approaches from dynamical system theory, statistical physics, time series analysis, or graph theory.The networks can range from a few to hundreds of billions of nodes, such as large communication networks or the brain. Connectivity in networks can vary widely, ranging from "all-to-all" to hierarchical or even sparse.When modeling realistic situations, time-delays must be often taken into account for the interactions in dynamical networks, as is the case in neural systems [6-9], laser networks [10-12], machine learning [13], traffic dynamics [14], and other applications. Particularly challenging are the situations in which the interplay between time-delays and network symmetries [15][16][17][18] or large delays [19-22] lead to new dynamical phenomena. They include synchronization [21,[23][24][25][26][27][28][29][30], explosive synchronization [31,32], various resonances [33], chimera states [24,34] and other patterns [35][36][37][38][39].The interplay between network topology and time-delayed interactions are also explored in [40,41].Many natural systems possess unstable states, and the stabilization of them might be of interest for applications. For example, stabilization of unstable equilibrium solution has application in semiconductor lasers [42], in nanoeletronics [43], in medicine [44], and others. An efficient strategy to control unstable periodic orbits, which is also applied to stabilization of equilibrium, is introducing a self-feedback delayed term. This approach is non-invasive, since the feedback term does not alter the original solutions. In particular, for stabilization of periodic orbits, the usual approach is to consider the delay equal or close to the period of the orbit, known as Pyragas control [45]. For stabilization of equilibrium, the aim can also be achieved with a suitable choice of delay [46,47].Here we consider a network model in which the nodes are interacting with a common time-delay.Hence, the delay is not an...

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Section: Introductionmentioning

confidence: 99%

Stabilization of synchronous equilibria in regular dynamical networks with delayed coupling

2023

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“…With the developments of the network era, the complex networks (CNs) have been widely used in various fields, such as power grids, 1 disease spread, 2 biological networks, 3 neural networks 4 and social networks 5 . It is worthwhile to mention that the CNs are composed of numerous nodes and edges with massive scales 6‐9 . In addition, there are some technical constraints in the research process so that the internal state information of the CNs cannot be obtained.…”

Section: Introductionmentioning

confidence: 99%

“…5 It is worthwhile to mention that the CNs are composed of numerous nodes and edges with massive scales. [6][7][8][9] In addition, there are some technical constraints in the research process so that the internal state information of the CNs cannot be obtained. Hence, the scholars have proposed various filter/state estimation (SE) methods to solve such issue which can estimate the unknown states based upon measurement information, thereby understanding and analyzing the dynamic rules of CNs more effectively.…”

Section: Introductionmentioning

confidence: 99%

Partial‐nodes‐based state estimation for state‐saturated complex networks with random mixed couplings under dynamic event‐triggered protocol

Lin

Chen

et al. 2023

Adaptive Control & Signal

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The state estimation (SE) problem is addressed for state-saturated complex networks (CNs) contaminated by the random mixed couplings. Such coupling phenomenon consists of the random inner coupling and the random outer coupling, where the random inner coupling is reflected by multiplicative noise and the random outer coupling is described by random variable obeying uniform distribution. In order to reduce resource waste and calculation cost, the additional auxiliary variable method is employed to construct the dynamic event-triggered communication condition, which can more effectively represent the change of information demand. Accordingly, a novel partial-nodes-based (PNB) estimator is designed in the presence of general nonlinearity and state-saturated nonlinearity, which can estimate the whole states of network nodes with the aid of the measurement information from partial nodes. The appropriate estimator gain is obtained to ensure that the upper bound of estimation error covariance (UBEEC) is minimized. Moreover, sufficient condition is given to guarantee that the trace of the UBEEC is uniformly bounded. Finally, the numerical example is presented to demonstrate the feasibility and effectiveness of the developed PNB estimation algorithm.

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“…Complex dynamical networks are indispensable for modeling many processes in nature, technology, and social sciences (Strogatz, 2001;Boccaletti et al, 2006;Arenas et al, 2008;Yanchuk et al, 2021). In realistic situations, collective dynamics in such networks is affected by the constraints on available resources from the environment (Roberts et al, 2014;Kroma-Wiley et al, 2021), resulting in complex dynamical phenomena, especially if the systems are self-organized to operate close to criticality (Levina et al, 2007).…”

Section: Introductionmentioning

confidence: 99%

Collective Activity Bursting in a Population of Excitable Units Adaptively Coupled to a Pool of Resources

Franović

Eydam

Yanchuk

et al. 2022

Front. Netw. Physiol.

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We study the collective dynamics in a population of excitable units (neurons) adaptively interacting with a pool of resources. The resource pool is influenced by the average activity of the population, whereas the feedback from the resources to the population is comprised of components acting homogeneously or inhomogeneously on individual units of the population. Moreover, the resource pool dynamics is assumed to be slow and has an oscillatory degree of freedom. We show that the feedback loop between the population and the resources can give rise to collective activity bursting in the population. To explain the mechanisms behind this emergent phenomenon, we combine the Ott-Antonsen reduction for the collective dynamics of the population and singular perturbation theory to obtain a reduced system describing the interaction between the population mean field and the resources.

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Dynamical phenomena in complex networks: fundamentals and applications

Cited by 8 publications

References 33 publications

Stabilization of synchronous equilibria in regular dynamical networks with delayed coupling

Stabilization of synchronous equilibria in regular dynamical networks with delayed coupling

Partial‐nodes‐based state estimation for state‐saturated complex networks with random mixed couplings under dynamic event‐triggered protocol

Collective Activity Bursting in a Population of Excitable Units Adaptively Coupled to a Pool of Resources

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