High-order couplings in geometric complex networks of neurons

Tlaie, A.; Leyva, I.; Sendiña‐Nadal, Irene

doi:10.1103/physreve.100.052305

Cited by 23 publications

(9 citation statements)

References 47 publications

(38 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, it was revealed that a single astrocyte can contact with up to 10 5 synapses without anatomical connections [40,47], which suggests that a latent higher-order interaction affects efficiently the signal propagation in neuronal system. Motivated by this fact, we assume that this higherorder effect originates from a huge group, like the ensemble system, and can adaptively modulate every specific neuron [48].…”

Section: Model and Analysismentioning

confidence: 99%

“…Nevertheless, the interactions in empirical systems may often involve in groups of entities (three or more). For instance, recent studies reveal that higher-order interactions are prevalent in plants and predatorprey ecosystems [37,38], social relationship networks [39], neural systems [40] and complicatedly coupled nonlinear oscillators systems [41]. Consideration of purely linear coupling may led to the wrong predictions because of the drawback that it cannot delineate the high-order effects.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Resonance induced by higher-order coupling diversity

Liu¹,

Wang²,

Wu³

et al. 2022

Preprint

View full text Add to dashboard Cite

The studies of collective oscillations induced by higher-order interactions point out the necessity of group effect in coupling modelization. As yet the related advances are mainly concentrated on nonlinear coupling patterns and cannot be straightforwardly extended to the linear ones. In present work, we introduce the standard deviation of dynamic behavior for the interacting group to complement the higher-order effect that beyond pairwise in diffusive coupling. By doing so, the higher-order effect can be flexibly extended to the linearly coupled system. We leverage this modelization to embrace the influence of heterogeneous higher-order coupling, including promoting and inhibiting effects, on the signal response for two conventional models, the globally coupled overdamped bistable oscillators and excitable FitzHugh-Nagumo neurons. Particularly, we numerically and analytically reveal that the optimal signal response can be obtained by an intermediate degree of higher-order coupling diversity for both systems. This resonant signal response stems from the competition between dispersion and aggregation induced by heterogeneous higher-order and positive pairwise couplings, respectively. Our results contribute to a better understanding of the signal propagation in linearly coupled systems.

show abstract

Section: Model and Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Resonance induced by higher-order coupling diversity

Liu¹,

Wang²,

Wu³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The Kuramoto model with higher-order interactions is known to describe topological structures such as higherorder simplexes or a simplicial complex [42,43], which are relevant to brain dynamics, neuronal networks, and biological transport networks [44,45]. In recent times, neuroscience studies have confirmed the existence of higher-order interactions between neurons.…”

Section: Modelmentioning

confidence: 99%

“…In recent times, neuroscience studies have confirmed the existence of higher-order interactions between neurons. For example, astrocytes and other glial cells are thought to be a biological source of high-order interactions since they interact with hundreds of synapses and actively regulate their activity [46,47].…”

Section: Modelmentioning

confidence: 99%

Influence of Asymmetric Parameters in Higher-Order Coupling With Bimodal Frequency Distribution

Manoranjani,

Gopal,

Senthilkumar

et al. 2022

Preprint

View full text Add to dashboard Cite

We investigate the phase diagram of the Sakaguchi-Kuramoto model with a higher order interaction along with the traditional pairwise interaction. We also introduce asymmetry parameters in both the interaction terms and investigate the collective dynamics and their transitions in the phase diagrams under both unimodal and bimodal frequency distributions. We deduce the evolution equations for the macroscopic order parameters and eventually derive pitchfork and Hopf bifurcation curves. Transition from the incoherent state to standing wave pattern is observed in the presence of the unimodal frequency distribution. In contrast, a rich variety of dynamical states such as the incoherent state, partially synchronized state-I, partially synchronized state-II, and standing wave patterns and transitions among them are observed in the phase diagram, via various bifurcation scenarios including saddle-node and homoclinic bifurcations, in the presence of bimodal frequency distribution. Higher order coupling enhances the spread of the bistable regions in the phase diagrams and also leads to the manifestation of bistability between incoherent and partially synchronized states even with unimodal frequency distribution, which is otherwise not observed with the pairwise coupling. Further, the asymmetry parameters facilitate the onset of several bistable and multistable regions in the phase diagrams. Very large values of the asymmetry parameters allow the phase diagrams to admit only the monostable dynamical states.

show abstract

“…However, this pairwise connectivity representation within layers may not always be able to illustrate the connection topology accurately among individual nodes. The neuronal system is an example where, on the one hand, individual neurons are connected via electrical and chemical synapses [54,61], and on the other hand, proof of many-body interactions between individual neurons have recently been found [7,[62][63][64]. Nevertheless, the interplay between higher-order structures and multilayer networks [65], under some aspects has yet to be investigated, and specifically, the study of synchronization is still in its early stages [66,67].…”

Section: Introductionmentioning

confidence: 99%

Stability of synchronization in simplicial complexes with multiple interaction layers

Anwar

Ghosh

2022

Phys. Rev. E

View full text Add to dashboard Cite

Understanding how the interplay between higher-order and multilayer structures of interconnections influences the synchronization behaviors of dynamical systems is a feasible problem of interest, with possible application in essential topics such as neuronal dynamics. Here, we provide a comprehensive approach for analyzing the stability of the complete synchronization state in simplicial complexes with numerous interaction layers. We show that the synchronization state exists as an invariant solution and derive the necessary condition for a stable synchronization state in presence of general coupling functions. It generalizes the well-known master stability function scheme to the higher-order structures with multiple interaction layers. We verify our theoretical results by employing them on networks of paradigmatic Rössler oscillators and Sherman neuronal models, and demonstrate that the presence of group interactions considerably improves the synchronization phenomenon in the multilayer framework.

show abstract

High-order couplings in geometric complex networks of neurons

Cited by 23 publications

References 47 publications

Resonance induced by higher-order coupling diversity

Resonance induced by higher-order coupling diversity

Influence of Asymmetric Parameters in Higher-Order Coupling With Bimodal Frequency Distribution

Stability of synchronization in simplicial complexes with multiple interaction layers

Contact Info

Product

Resources

About