Synchronization phenomena represent one of the central issues in the modern research, in
particular, on nonlinear dynamics, network science, and statistical physics with applications …

We demonstrate that chimera behavior can be observed in nonlocally coupled networks of
excitable systems in the presence of noise. This phenomenon is distinct from classical …

We propose an overview of the modeling approaches for the mathematical description and
analysis of processes that combine continuous and discontinuous behavior, namely …

Excitable systems with delayed feedback are important in areas from biology to
neuroscience and optics. They sustain multistable pulsing regimes with different numbers of …

A theoretical model of a network of neuron-like elements was constructed. The network
included several subnetworks. The first subnetwork was used to translate a constant …

We consider the macroscopic regimes and the scenarios for the onset and the suppression
of collective oscillations in a heterogeneous population of active rotators composed of …

In this note, we discuss the usage of the Dirac δ function in models of phase oscillators with
pulsatile inputs. Many authors use a product of the delta function and the phase response …

We investigate the relation between the dynamics of a single oscillator with delayed self-
feedback and a feed-forward ring of such oscillators, where each unit is coupled to its next …

Chaotic return maps are widely used to model various dynamical systems such as charged
particle movement, laser beam dynamic, celestial body orbiting and many others. Return …

We study the dynamics of an oscillatory system with pulse delayed feedback and noise of
two types:(i) phase noise acting on the oscillator and (ii) stochastic fluctuations of the …