## 3 Citations

Gradient and Hamiltonian coupled systems on undirected networks.

- Mathematics, Computer ScienceMathematical biosciences and engineering : MBE
- 2019

It is demonstrated with a neural network given by two groups of neurons that are mutually coupled through either excitatory or inhibitory synapses, which is modelled by a coupled system exhibiting both gradient and Hamiltonian structures.

Quotients and lifts of symmetric directed graphs.

- Mathematics
- 2018

Given a directed graph, an equivalence relation on the graph vertex set is said to be balanced if, for every two vertices in the same equivalence class, the number of directed edges from vertices of…

## References

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Complex Ginzburg-Landau equation on networks and its non-uniform dynamics

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Dynamics of the complex Ginzburg-Landau equation describing networks of diffusively coupled limit-cycle oscillators near the Hopf bifurcation is reviewed. It is shown that the Benjamin-Feir…

Hamiltonian mean field model: Effect of network structure on synchronization dynamics.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

The Hamiltonian mean field model of coupled inertial Hamiltonian rotors is a prototype for conservative dynamics in systems with long-range interactions where the interactions between the rotors are governed by a network described by a weighted adjacency matrix and it is found that the transition to synchrony begins when the coupling constant K is inversely proportional to the largest eigenvalue of the adjACency matrix.

Delay-induced Turing-like waves for one-species reaction-diffusion model on a network

- Mathematics
- 2015

A one-species time-delay reaction-diffusion system defined on a complex network is studied. Traveling waves are predicted to occur following a symmetry-breaking instability of a homogeneous…

Global feedback control of Turing patterns in network-organized activator-inhibitor systems

- Physics
- 2010

Results of the first systematic study on feedback control of nonequilibrium pattern formation in networks are reported. Effects of global feedback control on Turing patterns in network-organized…

Multiple-scale theory of topology-driven patterns on directed networks.

- PhysicsPhysical review. E
- 2016

The theory proves adequate versus simulations, as confirmed by operating with a paradigmatic reaction-diffusion model, and an effective equation for the nonlinear evolution of the amplitude of the most unstable mode, close to the threshold of criticality is derived.

Complex Networks: Structure and Dynamics

- Computer Science
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The major concepts and results recently achieved in the study of the structure and dynamics of complex networks are reviewed, and the relevant applications of these ideas in many different disciplines are summarized, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.

The theory of pattern formation on directed networks.

- MathematicsNature communications
- 2014

The theory of pattern formation in reaction-diffusion systems defined on symmetric networks is extended to the case of directed networks, which are found in a number of different fields, such as neuroscience, computer networks and traffic systems.