Related papers: Dirac synchronization is rhythmic and explosive
We propose Local Dirac Synchronization which uses the Dirac operator to capture the dynamics of coupled nodes and link signals on an arbitrary network. In Local Dirac Synchronization, the harmonic modes of the dynamics oscillate freely…
Designing stable cluster synchronization patterns is a fundamental challenge in nonlinear dynamics of networks with great relevance to understanding neuronal and brain dynamics. So far, cluster synchronization has been studied exclusively…
Synchronization is a fundamental dynamical state of interacting oscillators, observed in natural biological rhythms and in the brain. Global synchronization which occurs when non-linear or chaotic oscillators placed on the nodes of a…
Topological signals are dynamical variables not only defined on nodes but also on links of a network that are gaining significant attention in non-linear dynamics and topology and have important applications in brain dynamics. Here we show…
Simplicial complexes capture the underlying network topology and geometry of complex systems ranging from the brain to social networks. Here we show that algebraic topology is a fundamental tool to capture the higher-order dynamics of…
In dynamical systems on networks, one assigns the dynamics to nodes, which are then coupled via links. This approach does not account for group interactions and dynamics on links and other higher dimensional structures. Higher-order network…
The study of reaction-diffusion systems on networks is of paramount relevance for the understanding of nonlinear processes in systems where the topology is intrinsically discrete, such as the brain. Until now reaction-diffusion systems have…
Higher-order networks can sustain topological signals which are variables associated not only to the nodes, but also to the links, to the triangles and in general to the higher dimensional simplices of simplicial complexes. These…
Nowadays, explosive synchronization is a well documented phenomenon occurring in networks when the node frequency and its degree are correlated. This first-order transition, which may coexists with classical synchronization, has been…
We study a network of coupled logistic maps whose interactions occur with a certain distribution of delay times. The local dynamics is chaotic in the absence of coupling and thus the network is a paradigm of a complex system. There are two…
Topological signals are variables or features associated with both nodes and edges of a network. Recently, in the context of Topological Machine Learning, great attention has been devoted to signal processing of such topological signals.…
We define the topological Dirac equation describing the evolution of a topological wave function on networks or on simplicial complexes. On networks, the topological wave function describes the dynamics of topological signals or cochains,…
Synchrony is one of the most common dynamical states emerging on networks. The speed of convergence towards synchrony provides a fundamental collective time scale for synchronizing systems. Here we study the asymptotic synchronization times…
We study the relationship between topological scales and dynamic time scales in complex networks. The analysis is based on the full dynamics towards synchronization of a system of coupled oscillators. In the synchronization process, modular…
Synchronization of networked oscillators is known to depend fundamentally on the interplay between the dynamics of the graph's units and the microscopic arrangement of the network's structure. For non identical elements, the lack of…
We introduce the concept of dynamical score networks for the representation and analysis of tonal compositions: a score is interpreted as a dynamical network where every chord is a node and each progression links successive chords. This…
Collective synchronization in complex systems arises from the interplay between topology and dynamics, yet how to design and control such patterns in higher-order networks remains unclear. Here we show that a Dirac spectral programming…
A chaotic dynamics is typically characterized by the emergence of strange attractors with their fractal or multifractal structure. On the other hand, chaotic synchronization is a unique emergent self-organization phenomenon in nature.…
The synchronization of coupled chaotic systems represents a fundamental example of self organization and collective behavior. This well-studied phenomenon is classically characterized in terms of macroscopic parameters, such as Lyapunov…
We present a method based on symbolic dynamics for the detection of synchronization in networks of coupled maps and distinguishing between chaotic and random iterations. The symbolic dynamics are defined using special partitions of the…