Synchronization In Heterogeneous Networks Research Articles

The spark of synchronization in heterogeneous networks of chaotic maps.

We investigate the emergence of synchronization in heterogeneous networks of chaotic maps. Our findings reveal that a small cluster of highly connected maps is responsible for triggering the spark of synchronization. After the spark, the synchronized cluster grows in size and progressively moves to less connected maps, eventually reaching a cluster that may remain synchronized over time. We explore how the shape of the network degree distribution affects the onset of synchronization and derive an expression based on the network construction that determines the expected time for a network to synchronize. Understanding how the network design affects the spark of synchronization is particularly important for the control and design of more robust systems that require some level of coherence between a subset of units for better functioning. Numerical simulations in finite-sized networks are consistent with this analysis.

Rapid and robust synchronization via weak synaptic coupling

This paper examines how weak synaptic coupling can achieve rapid synchronization in heterogeneous networks. The assumptions aim at capturing the key mathematical properties that make this possible for biophysical networks. In particular, the combination of nodal excitability and synaptic coupling are shown to be essential to the phenomenon.

Emergence of chaotic cluster synchronization in heterogeneous networks.

Many real-world complex systems rely on cluster synchronization to function properly. A cluster of nodes exhibits synchronous behavior, while others behave erratically. Predicting the emergence of these clusters and understanding the mechanism behind their structure and variation in response to a parameter change is a daunting task in networks that lack symmetry. We unravel the mechanism for the emergence of cluster synchronization in heterogeneous random networks. We develop heterogeneous mean-field approximation together with a self-consistent theory to determine the onset and stability of the cluster. Our analysis shows that cluster synchronization occurs in a wide variety of heterogeneous networks, node dynamics, and coupling functions. The results could lead to a new understanding of the dynamical behavior of networks ranging from neural to social.

Synchronization in Networks with Nonlinearly Delayed Couplings on Example of Neural Mass Model

The problem of synchronization in heterogeneous networks of linear systems with nonlinear delayed diffusive coupling is considered. The network is presented in new coordinates mean-field dynamics and synchronization errors. Thus the problem of network synchronization is reduced to the studying of synchronization-error system stability. The circle criterion for time-delay systems is used to derive the stability conditions of synchronization-error system. Obtained results are applied to a network of neural mass model populations, and the synchronization conditions are established. Simulation results are provided to illustrate the obtained analytical results.

Explosive, continuous and frustrated synchronization transition in spiking Hodgkin–Huxley neural networks: The role of topology and synaptic interaction

Synchronization is an important collective phenomenon in interacting oscillatory agents. Many functional features of the brain are related to synchronization of neurons. The type of synchronization transition that may occur (explosive vs. continuous) has been the focus of intense attention in recent years, mostly in the context of phase oscillator models for which collective behavior is independent of the mean-value of natural frequency. However, synchronization properties of biologically-motivated neural models depend on the firing frequencies. In this study we report a systematic study of gamma-band synchronization in spiking Hodgkin–Huxley neurons which interact via electrical or chemical synapses. We use various network models in order to define the connectivity matrix. We find that the underlying mechanisms and types of synchronization transitions in gamma-band differs from beta-band. In gamma-band, network regularity suppresses transition while randomness promotes a continuous transition. Heterogeneity in the underlying topology does not lead to any change in the order of transition, however, correlation between number of synapses and frequency of a neuron will lead to explosive synchronization in heterogeneous networks with electrical synapses. Furthermore, small-world networks modeling a fine balance between clustering and randomness (as in the cortex), lead to explosive synchronization with electrical synapses, but a smooth transition in the case of chemical synapses. We also find that hierarchical modular networks, such as the connectome, lead to frustrated transitions. We explain our results based on various properties of the network, paying particular attention to the competition between clustering and long-range synapses.

Simple synchronization protocols for heterogeneous networks: beyond passivity

Abstract Synchronization among autonomous agents via local interactions is one of the benchmark problems in multi-agent control. Whereas synchronization algorithms for identical agents have been thoroughly studied, synchronization of heterogeneous networks still remains a challenging problem. The existing algorithms primarily use the internal model principle, assigning to each agent a local copy of some dynamical system (internal model). Synchronization of heterogeneous agents thus reduces to global synchronization of identical generators and local synchronization between the agents and their internal models. The internal model approach imposes a number of restrictions and leads to sophisticated dynamical (and, in general, nonlinear) controllers. At the same time, passive heterogeneous agents can be synchronized by a very simple linear protocol, which is used for consensus of first-order integrators. A natural question arises whether analogous algorithms are applicable to synchronization of agents that do not satisfy the passivity condition. In this paper, we study the synchronization problem for heterogeneous agents that are not passive but satisfy a weaker input feedforward passivity (IFP) condition. We show that such agents can also be synchronized by a simple linear protocol, provided that the interaction graph is strongly connected and the couplings are sufficiently weak. We demonstrate how stability of cooperative adaptive cruise control algorithms and some microscopic traffic flow models reduce to synchronization of heterogeneous IFP agents.

Non-Trivial Output Synchronization of Heterogeneous Passive Systems

In this technical note, we present conditions for non-trivial output synchronization in heterogeneous networks of passive linear systems. A network is said to be non-trivially output synchronized if its individual system outputs asymptotically converge to a common trajectory that is not identically zero. Though conditions for output synchronization in a heterogeneous network of passive systems have been revealed in previous literature, those conditions do not provide a criterion to check whether the network is synchronized trivially or non-trivially. Furthermore, we hardly found simulation results in the literature showing the non-trivial synchronization. In this technical note, we present necessary and sufficient conditions for the non-trivial output synchronization based on properties of passive linear systems and internal model principle. In addition, we present a systematic procedure for the realization of the internal model which fully satisfies the presented conditions.

Convergence and synchronization in heterogeneous networks of smooth and piecewise smooth systems

This paper presents a framework for the study of convergence in networks where the nodes’ dynamics may be both piecewise smooth and/or nonidentical. Sufficient conditions are derived for global convergence of all node trajectories towards the same bounded region in the synchronization error space. The analysis is based on the use of set-valued Lyapunov functions and bounds are derived on the minimum coupling strength required to make all nodes in the network converge towards each other. We also provide an estimate of the asymptotic bound on the mismatch between the node state trajectories. The analysis is performed both for linear and nonlinear coupling protocols. The theoretical analysis is extensively illustrated and validated via its application to a set of representative numerical examples.

Synchronization in heterogeneous networks of discrete‐time introspective right‐invertible agents

SUMMARYThis paper studies output synchronization problem, formation problem, and regulated synchronization problem for a heterogenous network of discrete‐time introspective right‐invertible agents. We first propose a decentralized control scheme to solve the output synchronization problem for a set of communication topologies. Moreover, if the synchronization trajectories are assumed to be bounded, a universal controller can be constructed for all communication topologies, which contain a directed spanning tree. The design can be applied to solve the formation problem with arbitrary formation vectors. In the regulated synchronization problem, we assume only the root receives information from exosystem. We then design a decentralized controller to solve the problem for a set of communication topologies. Copyright © 2013 John Wiley & Sons, Ltd.

High-Frequency Organization and Synchrony of Activity in the Purkinje Cell Layer of the Cerebellum

The cerebellum controls complex, coordinated, and rapid movements, a function requiring precise timing abilities. However, the network mechanisms that underlie the temporal organization of activity in the cerebellum are largely unexplored, because in vivo recordings have usually targeted single units. Here, we use tetrode and multisite recordings to demonstrate that Purkinje cell activity is synchronized by a high-frequency (approximately 200 Hz) population oscillation. We combine pharmacological experiments and modeling to show how the recurrent inhibitory connections between Purkinje cells are sufficient to generate these oscillations. A key feature of these oscillations is a fixed population frequency that is independent of the firing rates of the individual cells. Convergence in the deep cerebellar nuclei of Purkinje cell activity, synchronized by these oscillations, likely organizes temporally the cerebellar output.

Dynamical Weights and Enhanced Synchronization in Adaptive Complex Networks

Dynamical organization of connection weights is studied in scale-free networks of chaotic oscillators, where the coupling strength of a node from its neighbors develops adaptively according to the local synchronization property between the node and its neighbors. We find that when complete synchronization is achieved, the coupling strength becomes weighted and correlated with the topology due to a hierarchical transition to synchronization in heterogeneous networks. Importantly, such an adaptive process enhances significantly the synchronizability of the networks, which could have meaningful implications in the manipulation of dynamical networks.

Resonant Synchronization in Heterogeneous Networks of Inhibitory Neurons

Brain rhythms arise through the synchronization of neurons and their entrainment in a regular firing pattern. In this process, networks of reciprocally connected inhibitory neurons are often involved, but what mechanism determines the oscillation frequency is not completely understood. Analytical studies predict that the emerging frequency band is primarily constrained by the decay rate of the unitary IPSC. We observed a new phenomenon of resonant synchronization in computer-simulated networks of inhibitory neurons in which the synaptic current has a delayed onset, reflecting finite spike propagation and synaptic transmission times. At the resonant level of network excitation, all neurons fire synchronously and rhythmically with a period approximately four times the mean delay of the onset of the inhibitory synaptic current. The amplitude and decay time constant of the synaptic current have relatively minor effects on the emerging frequency band. By varying the axonal delay of the inhibitory connections, networks with a realistic synaptic kinetics can be tuned to frequencies from 40 to >200 Hz. This resonance phenomenon arises in heterogeneous networks with, on average, as few as five connections per neuron. We conclude that the delay of the synaptic current is the primary parameter controlling the oscillation frequency of inhibitory networks and propose that delay-induced synchronization is a mechanism for fast brain rhythms that depend on intact inhibitory synaptic transmission.