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Many real-world complex systems rely on cluster synchronization to function properly. A cluster of nodes exhibits synchronous behavior while others behave erratically. Predicting the emergence of these clusters and understanding the…
A network of coupled time-varying systems, where individual nodes are interconnected through links, is a modeling framework widely used by many disciplines. For identical nodes displaying a complex behavior known as chaos, clusters of nodes…
Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network's automorphism group,…
We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in real space, with quasi-exponentially…
The brain's structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world…
Dynamical symmetry breaking in an expanding nuclear system is investigated in semi-classical and quantum framework by employing a collective transport model which is constructed to mimic the collective behavior of expanding systems. It is…
In the brain, coherent neuronal activities often appear simultaneously in multiple frequency bands, e.g., as combinations of alpha (8-12 Hz), beta (12.5-30 Hz), gamma (30-120 Hz) oscillations, among others. These rhythms are believed to…
Kuramoto oscillators have been proposed earlier as a model for interacting systems that exhibit synchronisation. In this article we study the difference between networks with symmetric and asymmetric distribution of natural frequencies. We…
Synchrony patterns describe network states in which nodes of a coupled dynamical system are grouped into clusters based on synchronization between nodes. Beyond simple synchrony, synchronized clusters may also exhibit active or inactive…
Spontaneous cortical population activity exhibits a multitude of oscillatory patterns, which often display synchrony during slow-wave sleep or under certain anesthetics and stay asynchronous during quiet wakefulness. The mechanisms behind…
We investigate the connection between the dynamics of synchronization and the modularity on complex networks. Simulating the Kuramoto's model in complex networks we determine patterns of meta-stability and calculate the modularity of the…
We analyze the 3-parameter family of random networks which are uniform on networks with fixed number of edges, triangles, and nodes (between 33 and 66). We find precursors of phase transitions which are known to be present in the asymptotic…
Despite the fact that the phenomenon of bursting activity is important for functioning of living neural networks, the mechanisms of its origin are still not clear. In this paper, we propose a new phenomenological model that can explain the…
Although recent neurophysiological experiments suggest that synchronous neural activity is involved in some perceptual and cognitive processes, the functional role of such coherent neuronal behavior is not well understood. As a first step…
Hopf bifurcation in networks of coupled ODEs creates periodic states in which the relative phases of nodes are well defined near bifurcation. When the network is a fully inhomogeneous nearest-neighbour coupled unidirectional ring, and node…
Asymmetry in the synaptic interactions between neurons plays a crucial role in determining the memory storage and retrieval properties of recurrent neural networks. In this work, we analyze the problem of storing random memories in a…
By Avila's global theory, we analytically reveal that the non-Hermitian mobility edge will take on a ring structure in the complex plane, which we name as "mobility ring". The universality of mobility ring has been checked and supported by…
Networks of model neurons with balanced recurrent excitation and inhibition produce irregular and asynchronous spiking activity. We extend the analysis of balanced networks to include the known dependence of connection probability on the…
Turing instability in activator-inhibitor systems provides a paradigm of nonequilibrium pattern formation; it has been extensively investigated for biological and chemical processes. Turing pattern formation should furthermore be possible…
Synchronization of neural activity in the gamma frequency band is associated with various cognitive phenomena. Abnormalities of gamma synchronization may underlie symptoms of several neurological and psychiatric disorders such as…