Synchronization in adaptive weighted networks

Adaptive coupling between neurons widens the entrainment range of the suprachiasmatic nucleus

In many realistic systems, such as neural networks in the brain, the coupling strength between neurons is not fixed, but adaptively adjusts according to their activities. The suprachiasmatic nucleus (SCN), as the main clock in the mammalian brain, has been found to be a plastic neural network, and the coupling strength between neurons is highly dynamical. An important function of the SCN is entrainment, reflecting the ability of the SCN to synchronize with the external light-dark cycle. The entrainment ability is reflected by the entrainment range, which is a period range for the external light-dark cycle to which the SCN can entrain. In this article, we investigated whether the entrainment range of the SCN is affected by the adaptive coupling. We use a modified Kuramoto model with external light-dark cycle. We found that when the light sensitivity is larger than the fixed coupling strength (the coupling strength without adaptive rules), adaptive coupling can widen the entrainment range. Our findings help to understand the impact of the adaptive coupling between oscillatorty neurons on the collective behavior of the SCN, and provides a possible explanation for the plasticity of coupling in the master clock network.

Synchronization transitions induced by the fluctuation of adaptive coupling strength in delayed Newman-Watts neuronal networks

Introducing adaptive coupling in delayed neuronal networks and regulating the dissipative parameter (DP) of adaptive coupling by noise, we study the effect of fluctuations of the changing rate of adaptive coupling on the synchronization of the neuronal networks. It is found that time delay can induce synchronization transitions for intermediate DP values, and the synchronization transitions become strongest when DP is optimal. As the intensity of DP noise is varied, the neurons can also exhibit synchronization transitions, and the phenomenon is delay-dependent and is enhanced for certain time delays. Moreover, the synchronization transitions change with the change of DP and become strongest when DP is optimal. These results show that randomly changing adaptive coupling can considerably change the synchronization of the neuronal networks, and hence could play a crucial role in the information processing and transmission in neural systems.

Adaptive coupling optimized spiking coherence and synchronization in Newman-Watts neuronal networks

In this paper, we have numerically studied the effect of adaptive coupling on the temporal coherence and synchronization of spiking activity in Newman-Watts Hodgkin-Huxley neuronal networks. It is found that random shortcuts can enhance the spiking synchronization more rapidly when the increment speed of adaptive coupling is increased and can optimize the temporal coherence of spikes only when the increment speed of adaptive coupling is appropriate. It is also found that adaptive coupling strength can enhance the synchronization of spikes and can optimize the temporal coherence of spikes when random shortcuts are appropriate. These results show that adaptive coupling has a big influence on random shortcuts related spiking activity and can enhance and optimize the temporal coherence and synchronization of spiking activity of the network. These findings can help better understand the roles of adaptive coupling for improving the information processing and transmission in neural systems.

Effects of adaptive coupling on stochastic resonance of small-world networks

The phenomenon of stochastic resonance in networks with small-world connectivity is investigated when the coupling strength is adaptive. The effects of the fixed and adaptive couplings on stochastic resonance of the system are discussed. It is found that the resonance is a monotonically increasing function of the adaptive coupling strength, while there is a peak when the coupling strength is fixed. The resonance for the adaptive coupling can reach a much larger value than that for fixed coupling.

Adaptive dynamical networks via neighborhood information: synchronization and pinning control

In this paper, we introduce a model of an adaptive dynamical network by integrating the complex network model and adaptive technique. In this model, the adaptive updating laws for each vertex in the network depend only on the state information of its neighborhood, besides itself and external controllers. This suggests that an adaptive technique be added to a complex network without breaking its intrinsic existing network topology. The core of adaptive dynamical networks is to design suitable adaptive updating laws to attain certain aims. Here, we propose two series of adaptive laws to synchronize and pin a complex network, respectively. Based on the Lyapunov function method, we can prove that under several mild conditions, with the adaptive technique, a connected network topology is sufficient to synchronize or stabilize any chaotic dynamics of the uncoupled system. This implies that these adaptive updating laws actually enhance synchronizability and stabilizability, respectively. We find out that even though these adaptive methods can succeed for all networks with connectivity, the underlying network topology can affect the convergent rate and the terminal average coupling and pinning strength. In addition, this influence can be measured by the smallest nonzero eigenvalue of the corresponding Laplacian. Moreover, we provide a detailed study of the influence of the prior parameters in this adaptive laws and present several numerical examples to verify our theoretical results and further discussion.