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Chimera states are complex spatiotemporal patterns consisting of coexisting domains of coherence and incoherence. We study networks of nonlocally coupled logistic maps and analyze systematically how the dilution of the network links…
One of the simplest mathematical models in the study of nonlinear systems is the Kuramoto model, which describes synchronization in systems from swarms of insects to superconductors. We have recently found a connection between the original,…
Synchronization in networks of oscillatory units is an emergent phenomenon present in various systems, such as biological, technological, and social systems. Many real-world systems have adaptive properties, meaning that their…
Chimera states, namely the coexistence of coherent and incoherent behavior, were previously analyzed in complex networks. However, they have not been extensively studied in modular networks. Here, we consider the neural network of the…
Nonlinear systems possessing nonattracting chaotic sets, such as chaotic saddles, embedded in their state space may oscillate chaotically for a transient time before eventually transitioning into some stable attractor. We show that these…
Chimeras are surprising yet important states in which domains of decoherent (asynchronous) and coherent (synchronous) oscillations co-exist. In this article, we report on the discovery of a new class of chimeras, called {\it mixed-amplitude…
The emergence and nature of amplitude mediated chimera states, spatio-temporal patterns of co-existing coherent and incoherent regions, are investigated for a globally coupled system of active and inactive Ginzburg-Landau oscillators. The…
We consider two coupled populations of leaky integrate-and-fire neurons. Depending on the coupling strength, mean fields generated by these populations can have incommensurate frequencies, or become frequency locked. In the observed 2:1…
The phenomenon of explosive synchronization, which originates from hypersensitivity to small perturbation caused by some form of frustration prevailed in various physical and biological systems, has been shown to lead events of cascading…
Chimera and Solitary states have captivated scientists and engineers due to their peculiar dynamical states corresponding to the co-existence of coherent and incoherent dynamical evolution in coupled units in various natural and artificial…
We show that chimera patterns can be induced by noise in nonlocally coupled neural networks in the excitable regime. In contrast to classical chimeras, occurring in noise-free oscillatory networks, they have features of two phenomena:…
Chimera states in networks of coupled oscillators occur when some fraction of the oscillators synchronise with one another, while the remaining oscillators are incoherent. Several groups have studied chimerae in networks of identical…
When chaotic oscillators are coupled in complex networks a number of interesting synchronization phenomena emerge. Notable examples are the frequency and amplitude chimeras, chimera death states, solitary states as well as combinations of…
Chimera states in systems of nonlocally coupled oscillators, i.e., self-organized coexistence of coherent and incoherent oscillator populations, have attracted much attention. In this study, we consider the effect of frequency…
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 study a triangular network of three populations of coupled phase oscillators with identical frequencies. The populations interact nonlocally, in the sense that all oscillators are coupled to one another, but more weakly to those in…
We explore numerically the impact of additive Gaussian noise on the spatio-temporal dynamics of ring networks of nonlocally coupled chaotic maps. The local dynamics of network nodes is described by the logistic map, the Ricker map, and the…
In this work a new mathematical model for complex neural networks is presented by the partly diffusive FitzHugh-Nagumo equations with ensemble boundary coupling. We analyze the dissipative dynamics and boundary coupling dynamics of the…
The problem of synchronization in heterogeneous networks of linear systems with nonlinear delayed diffusive coupling is considered. The network is presented in new coordinates mean-field dynamics and synchronization errors. Thus the problem…
The human brain is a complex dynamical system that gives rise to cognition through spatiotemporal patterns of coherent and incoherent activity between brain regions. As different regions dynamically interact to perform cognitive tasks,…