Solitary states in multiplex neural networks: Onset and vulnerability

Schülen, Leonhard; Janzen, David A.; Medeiros, Everton S.; Zakharova, Anna

doi:10.1016/j.chaos.2021.110670

Cited by 26 publications

(7 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They do not wander in space and mathematically, are Lyapunov stable states (standing waves) in the system phase space. Recently, the existence of the solitary states has been also reported in small networks [27], adaptive [29], multiplex [30], and power grid [15] systems, as well as in the mean-field limit [31].…”

Section: Introductionmentioning

confidence: 91%

Chimera states for directed networks

Jaros

Левченко

Kapitaniak

et al. 2021

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

We demonstrate that chimera behavior can be observed in ensembles of phase oscillators with unidirectional coupling. For a small network consisting of only three identical oscillators (cyclic triple), tiny chimera islands arise in the parameter space. They are surrounded by developed chaotic switching behavior caused by a collision of rotating waves propagating in opposite directions. For larger networks, as we show for hundred oscillators (cyclic century), the islands merge into a single chimera continent which incorporates the world of chimeras of different configuration. The phenomenon inherits from networks with intermediate ranges of the unidirectional coupling and it diminishes as it decreases.

show abstract

Section: Introductionmentioning

confidence: 91%

Chimera states for directed networks

Jaros

Левченко

Kapitaniak

et al. 2021

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

show abstract

“…[34] In special cases, while most of the neurons are synchronous, a few scatter from the total synchronized ones. [35] The few neurons that split off from the synchronized ones are named solitary ones and this behavior is called the solitary state. [35] The chimera state is another collective behavior among neurons that has been the center of attention of many researchers.…”

Section: Introductionmentioning

confidence: 99%

Collective behavior of cortico-thalamic circuits: Logic gates as the thalamus and a dynamical neuronal network as the cortex

Bahramian¹,

Jamal²,

Parastesh³

et al. 2022

Chinese Phys. B

View full text Add to dashboard Cite

This paper introduces a two-layer network to investigate the effects of cortico-thalamic circuits on the cortexʼs collective behavior. In the brain, different parts of the cortex collaborate to process information. One of the main parts, which is the path of different cortex contacts, is the thalamus whose circuit is referred to as the “vertical” cortico-thalamic connectivity. Thalamus subnuclei can participate in the processing of the information that passes through them. It has been shown that they play the functional role of logic gates (AND, OR and XOR). To study how these thalamus circuits affect the cortical neuron behavior, a two-layer network is proposed wherein the cortex layer is composed of Hindmarsh–Rose models and the thalamus layer is constructed with logic gates. Results show that considering these logic gates can lead the network towards different synchronization, asynchronization, chimera and solitary patterns. It is revealed that for AND-gate and OR-gate, increasing the number of gates or their outputs can increase and decrease the networkʼs coherency in excitatory and inhibitory cases, respectively. However, considering XOR-gates always results in the chimera state.

show abstract

“…it is the sole network attractor 10,11,21 . Conversely, in sparse networks, the ISS is often sharing the system state-space with other synchronization patterns such as q-twisted states 10,22,23 , traveling waves [23][24][25] , solitary and chimera states [26][27][28][29] . In such a scenario, the ISS possess a domain of attraction, i.e., a finite portion of the network state-space from where all trajectories converge to the ISS.…”

Section: Introductionmentioning

confidence: 99%

Sparsity-driven synchronization in oscillators networks

Mihara,

Medeiros,

Zakharova

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

The emergence of synchronized behavior is a direct consequence of networking dynamical systems. Naturally, strict instances of this phenomenon, such as the states of complete synchronization are favored, or even ensured, in networks with a high density of connections. Conversely, in sparse networks, the system state-space is often shared by a variety of coexistent solutions. Consequently, the convergence to complete synchronized states is far from being certain. In this scenario, we report the surprising phenomenon in which completely synchronized states are made the sole attractor of sparse networks by removing network links, the sparsity-driven synchronization. This phenomenon is observed numerically for nonlocally coupled Kuramoto networks and verified analytically for locally coupled ones. In addition, we reduce the network equations to a one-dimension dynamical system to unravel the bifurcation scenario underlying the network transition to completely synchronized behavior. Furthermore, we present a simple procedure, based on the bifurcations in the thermodynamic limit, that determines the minimum number of links to be removed in order to ensure complete synchronization. Finally, we propose an application of the reported phenomenon as a control scheme to drive complete synchronization in high connectivity networks.

show abstract

Solitary states in multiplex neural networks: Onset and vulnerability

Cited by 26 publications

References 35 publications

Chimera states for directed networks

Chimera states for directed networks

Collective behavior of cortico-thalamic circuits: Logic gates as the thalamus and a dynamical neuronal network as the cortex

Sparsity-driven synchronization in oscillators networks

Contact Info

Product

Resources

About