Bifurcations and Synchronization in Networks of Unstable Reaction–Diffusion Systems

Miranville, Alain; Cantin, Guillaume; Aziz-Alaoui, M. A.

doi:10.1007/s00332-021-09701-9

Cited by 5 publications

(5 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Next, assumption (25) means that the nodes i and j admit only common neighbors, which implies that M i,j = M j,i = ∅ and S i,j = N i \ {j } = N j \ {i }, where the sets M i,j , M j,i and S i,j are defined in lemma 3. Therefore, we can apply lemma 3 and we obtain…”

Section: Lemmamentioning

confidence: 99%

“…In [11], it has been proved that the spatial diffusion of individuals in such meta-population models acts as a combination of short and long range diffusion. In parallel, the dynamics of chemical reactions networks have been studied in [14], [15] via the entropy framework; synchronization of unstable patterns in other chemical reactions networks has been investigated in [25]. It is observed that the main research axis which motivates these works is very often related to the synchronization phenomenon.…”

Section: Related Workmentioning

confidence: 99%

“…Our third simulation explores the case of a small four nodes network, whose underlying graph is complete, so that assumption (25) is fulfilled for each pair of nodes. We vary the geometry of the domains by considering egg-shape domains, as depicted in Figure 8.…”

Section: Four Domains Complete Graph Networkmentioning

confidence: 99%

“…Let assumptions (18), (39) and (40) hold. Suppose moreover that two neighbor nodes i and j of the complex network ( 2)-( 4) and (10) satisfy equation (25) and the following conditions:…”

mentioning

confidence: 99%

See 3 more Smart Citations

Synchronization of Turing patterns in complex networks of reaction–diffusion systems set in distinct domains

Aziz-Alaoui,

Cantin,

Thorel

2024

Nonlinearity

Self Cite

View full text Add to dashboard Cite

We present an innovative complex network of reaction–diffusion systems set in distinct domains, with boundary couplings. The complex network models the evolution of interacting populations living in a heterogeneous and fragmented habitat, whose biological individuals migrate from one patch to another. In our model, the displacements of individuals are described by mixed boundary couplings, involving both the Neumann and Robin boundary conditions, which improve the modeling of migrations by point-wise couplings. We investigate the cases of diffusion in isotropic and anisotropic habitats and establish original sufficient conditions of synchronization in this complex network model, for complete graphs, cyclic graphs and rings of nearest neighbors. In parallel, we apply our theoretical framework to a nonlinear predator–prey model with Leslie–Gower-type functional response and explore numerically the emergence of synchronization on heterogeneous Turing patterns.

show abstract

Section: Lemmamentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Four Domains Complete Graph Networkmentioning

confidence: 99%

“…Let assumptions (18), (39) and (40) hold. Suppose moreover that two neighbor nodes i and j of the complex network ( 2)-( 4) and (10) satisfy equation (25) and the following conditions:…”

mentioning

confidence: 99%

See 2 more Smart Citations

Synchronization of Turing patterns in complex networks of reaction–diffusion systems set in distinct domains

Aziz-Alaoui,

Cantin,

Thorel

2024

Nonlinearity

Self Cite

View full text Add to dashboard Cite

show abstract

“…Network synchronization has been always concerned by scholars and has involved in many fields, such as mathematics, physics, biological and social science [1][2][3]. The research on synchronization starts from singlelayer network [4] and gradually expands to multi-layer network.…”

Section: Introductionmentioning

confidence: 99%

Synchronizability of Generalized Two-layer Networks with Different Layer Topologies

Lian

2023

JAMCS

View full text Add to dashboard Cite

This paper focuses on a generalized two-layer network and its synchronizability, which randomly generate different topologies at each layer. This kind of network can better describe some irregular networks in reality. From the master stability function method of network synchronization analysis, we estimate the largest eigenvalue and the lowest nonzero eigenvalue of the supra-Laplacian matrix. Then, the influence of node coupling strength on the synchronizability of generalized two-layer networks is analyzed. We obtain that the enhancement of node coupling strength can promote network synchronization in bounded and unbounded synchronization regions. In the end, we perform numerical simulations based on theoretical analysis. The numerical results also show that the more nodes, the stronger the synchronizability under the unbounded synchronization region, and the opposite is true for the bounded synchronization region. The results have a certain guiding significance for the synchronous application of general network in reality.

show abstract

Uniform ultimate boundedness and approximate synchronization of coupled reaction-diffusion systems with parameter mismatches

Tseng

2024

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

Bifurcations and Synchronization in Networks of Unstable Reaction–Diffusion Systems

Cited by 5 publications

References 26 publications

Synchronization of Turing patterns in complex networks of reaction–diffusion systems set in distinct domains

Synchronization of Turing patterns in complex networks of reaction–diffusion systems set in distinct domains

Synchronizability of Generalized Two-layer Networks with Different Layer Topologies

Uniform ultimate boundedness and approximate synchronization of coupled reaction-diffusion systems with parameter mismatches

Contact Info

Product

Resources

About