Synchronization in heterogeneous FitzHugh-Nagumo networks with hierarchical architecture

Abstract

We study synchronization in heterogeneous FitzHugh-Nagumo networks. It is well known that heterogeneities in the nodes hinder synchronization when becoming too large. Here, we develop a controller to counteract the impact of these heterogeneities. We first analyze the stability of the equilibrium point in a ring network of heterogeneous nodes. We then derive a sufficient condition for synchronization in the absence of control. Based on these results we derive the controller providing synchronization for parameter values where synchronization without control is absent. We demonstrate our results in networks with different topologies. Particular attention is given to hierarchical (fractal) topologies, which are relevant for the architecture of the brain.

Reaction Time Improvements by Neural Bistability

“…Rathelot et al [3] paved the way for RTs reduction to gain in the future. This scenario is supported by Reference [94] and by reversed application of Plotnikov’s [95] adaptive control without prior knowledge of parameters, or search of independent FHN model coefficients [96] and by estimating these very accurately for the models [97].…”

FitzHugh–Nagumo oscillators on complex networks mimic epileptic-seizure-related synchronization phenomena

“…59,60 The white matter tracts in the human brain were reported to have a quasi-fractal structure. 61,62 This inspired simulations of networks of FHN oscillators with a one-dimensional [63][64][65][66] or two-dimensional 30,67 fractal coupling structure, and also for other dynamical models. [68][69][70][71][72][73] To create a (onedimensional) ring network with fractal connectivity, we follow the procedure described in Ref.…”

Layered Synchronization and Identification of Uncertain Delayed Hierarchical Networks

“…Remark 2. Previous research results focus on the innovation of synchronization schemes while overlooking the more practical combined design of hierarchical control and dual identification [20][21][22][23][24]. Hierarchical control is employed in 3D networks, while dual identification is applied when dynamics nodes and hierarchical topology need to be identified during the process of layered control.…”

“…A lot of research into the hierarchical network has been achieved in recent years on the exploration of the specific structures and interactional ways of multilevel, multidimensional, and multiplex networks, which reflects the transitional trend of network modeling structure from the plane to the stereoscopic. e self-structuring algorithm has been proposed to solve the high-dimensional problems in the hierarchical neural network [19]; the asynchronous and intermittent sampled-data controllers have been studied to control a kind of hierarchical time-varying neural networks [20]; the finite-time synchronization in coupled hierarchical hybrid neural networks has been concerned [21]; the synchronization control on heterogeneous FitzHugh-Nagumo networks with hierarchical topologies has been studied [22]; the new reinforcement learning algorithm has been designed to realize hierarchical optimal synchronization [23]; the real brain hierarchical modular organization has been found during the brain processing with diverse functional interactions [24]; however, the hierarchical network of combining chain structure with global structure is not considered. Likewise, plenty of identification methods are confined to the identification of parameters or network topology [25][26][27].…”