Collective dynamics and shot-noise-induced switching in a two-population neural network.

Neural mass models are a powerful tool for modeling of neural populations. Such models are often used as building blocks for the simulation of large-scale neural networks and the whole brain. Here, we carry out systematic bifurcation analysis of a neural mass model for the basic motif of various neural circuits, a system of two populations, an excitatory, and an inhibitory ones.

Adaptive myelination causes slow oscillations in recurrent neural loops.

The brain is known to be plastic, i.e., capable of changing and reorganizing as it develops and accumulates experience.

Constructive role of shot noise in the collective dynamics of neural networks.

Finite-size effects may significantly influence the collective dynamics of large populations of neurons. Recently, we have shown that in globally coupled networks these effects can be interpreted as additional common noise term, the so-called shot noise, to the macroscopic dynamics unfolding in the thermodynamic limit. Here, we continue to explore the role of the shot noise in the collective dynamics of globally coupled neural networks.

Shot noise in next-generation neural mass models for finite-size networks.

Neural mass models is a general name for various models describing the collective dynamics of large neural populations in terms of averaged macroscopic variables. Recently, the so-called next-generation neural mass models have attracted a lot of attention due to their ability to account for the degree of synchrony. Being exact in the limit of infinitely large number of neurons, these models provide only an approximate description of finite-size networks.

Noise-induced switching in an oscillator with pulse delayed feedback: A discrete stochastic modeling approach.

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 feedback delay. Using an event-based approach, we reduce the system dynamics to a stochastic discrete map. For weak noise, we find that the oscillator fluctuates around a deterministic state, and we derive an autoregressive model describing the system dynamics.

Applying interval stability concept to empirical model of middle Pleistocene transition.

Interval stability is a novel method for the study of complex dynamical systems, allowing for the estimation of their stability to strong perturbations. This method describes how large perturbation should be to disrupt the stable dynamical regime of the system (attractor). In our work, interval stability is used for the first time to study the properties of a real natural system: to analyze the stability of the earth's climate system during the last 2.

Noise-induced dynamical regimes in a system of globally coupled excitable units.

We study the interplay of global attractive coupling and individual noise in a system of identical active rotators in the excitable regime. Performing a numerical bifurcation analysis of the nonlocal nonlinear Fokker-Planck equation for the thermodynamic limit, we identify a complex bifurcation scenario with regions of different dynamical regimes, including collective oscillations and coexistence of states with different levels of activity. In systems of finite size, this leads to additional dynamical features, such as collective excitability of different types and noise-induced switching and bursting.

Effect of noise on the collective dynamics of a heterogeneous population of active rotators.

We study the collective dynamics of a heterogeneous population of globally coupled active rotators subject to intrinsic noise. The theory is constructed on the basis of the circular cumulant approach, which yields a low-dimensional model reduction for the macroscopic collective dynamics in the thermodynamic limit of an infinitely large population. With numerical simulation, we confirm a decent accuracy of the model reduction for a moderate noise strength; in particular, it correctly predicts the location of the bistability domains in the parameter space.

Reduction of the collective dynamics of neural populations with realistic forms of heterogeneity.

Reduction of collective dynamics of large heterogeneous populations to low-dimensional mean-field models is an important task of modern theoretical neuroscience. Such models can be derived from microscopic equations, for example with the help of Ott-Antonsen theory. An often used assumption of the Lorentzian distribution of the unit parameters makes the reduction especially efficient.

On the interpretation of Dirac δ pulses in differential equations for phase oscillators.

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 curve in the right-hand side of an ordinary differential equation to describe the discontinuous phase dynamics in such systems. We point out that this notation has to be treated with care as it is ambiguous.

Mode Hopping in Oscillating Systems with Stochastic Delays.

We study a noisy oscillator with pulse delayed feedback, theoretically and in an electronic experimental implementation. Without noise, this system has multiple stable periodic regimes. We consider two types of noise: (i) phase noise acting on the oscillator state variable and (ii) stochastic fluctuations of the coupling delay.

Two scenarios for the onset and suppression of collective oscillations in heterogeneous populations of active rotators.

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 excitable or oscillatory elements. We analyze the system in the continuum limit within the framework of Ott-Antonsen reduction method, determining the states with a constant mean field and their stability boundaries in terms of the characteristics of the rotators' frequency distribution. The system is established to display three macroscopic regimes, namely the homogeneous stationary state, where all the units lie at the resting state, the global oscillatory state, characterized by the partially synchronized local oscillations, and the heterogeneous stationary state, which includes a mixture of resting and asynchronously oscillating units.

Itinerant chimeras in an adaptive network of pulse-coupled oscillators.

In a network of pulse-coupled oscillators with adaptive coupling, we discover a dynamical regime which we call an "itinerant chimera." Similarly as in classical chimera states, the network splits into two domains, the coherent and the incoherent. The drastic difference is that the composition of the domains is volatile, i.

Clustering promotes switching dynamics in networks of noisy neurons.

Macroscopic variability is an emergent property of neural networks, typically manifested in spontaneous switching between the episodes of elevated neuronal activity and the quiescent episodes. We investigate the conditions that facilitate switching dynamics, focusing on the interplay between the different sources of noise and heterogeneity of the network topology. We consider clustered networks of rate-based neurons subjected to external and intrinsic noise and derive an effective model where the network dynamics is described by a set of coupled second-order stochastic mean-field systems representing each of the clusters.

Embedding the dynamics of a single delay system into a feed-forward ring.

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 neighbor in the same way as in the self-feedback case. We show that periodic solutions of the delayed oscillator give rise to families of rotating waves with different wave numbers in the corresponding ring. In particular, if for the single oscillator the periodic solution is resonant to the delay, it can be embedded into a ring with instantaneous couplings.

Event-based simulation of networks with pulse delayed coupling.

Pulse-mediated interactions are common in networks of different nature. Here we develop a general framework for simulation of networks with pulse delayed coupling. We introduce the discrete map governing the dynamics of such networks and describe the computation algorithm for its numerical simulation.

Dynamical regimes of four oscillators with excitatory pulse coupling.

The dynamical regimes of four almost identical oscillators with pulsatile excitatory coupling have been studied theoretically with two models: a kinetic model of the Belousov-Zhabotinsky reaction and a phase-reduced model. Unidirectional coupling on a ring and all-to-all coupling have been considered. The time delay τ between the moments of a spike in one oscillator and a pulse perturbation of the other(s) plays a crucial role in the emergence of the dynamical modes, which are classified as regular, complex, and OS (oscillation-suppression)-modes.

Jittering waves in rings of pulse oscillators.

Rings of oscillators with delayed pulse coupling are studied analytically, numerically, and experimentally. The basic regimes observed in such rings are rotating waves with constant interspike intervals and phase lags between the neighbors. We show that these rotating waves may destabilize leading to the so-called jittering waves.

Phase response curves for models of earthquake fault dynamics.

We systematically study effects of external perturbations on models describing earthquake fault dynamics. The latter are based on the framework of the Burridge-Knopoff spring-block system, including the cases of a simple mono-block fault, as well as the paradigmatic complex faults made up of two identical or distinct blocks. The blocks exhibit relaxation oscillations, which are representative for the stick-slip behavior typical for earthquake dynamics.

Dynamical regimes of four almost identical chemical oscillators coupled via pulse inhibitory coupling with time delay.

The dynamic regimes in networks of four almost identical spike oscillators with pulsatile coupling via inhibitor are systematically studied. We used two models to describe individual oscillators: a phase-oscillator model and a model for the Belousov-Zhabotinsky reaction. A time delay τ between a spike in one oscillator and the spike-induced inhibitory perturbation of other oscillators is introduced.

Mean-field dynamics of a random neural network with noise.

We consider a network of randomly coupled rate-based neurons influenced by external and internal noise. We derive a second-order stochastic mean-field model for the network dynamics and use it to analyze the stability and bifurcations in the thermodynamic limit, as well as to study the fluctuations due to the finite-size effect. It is demonstrated that the two types of noise have substantially different impact on the network dynamics.

Emergence and combinatorial accumulation of jittering regimes in spiking oscillators with delayed feedback.

Interaction via pulses is common in many natural systems, especially neuronal. In this article we study one of the simplest possible systems with pulse interaction: a phase oscillator with delayed pulsatile feedback. When the oscillator reaches a specific state, it emits a pulse, which returns after propagating through a delay line.

Multistable jittering in oscillators with pulsatile delayed feedback.

Oscillatory systems with time-delayed pulsatile feedback appear in various applied and theoretical research areas, and received a growing interest in recent years. For such systems, we report a remarkable scenario of destabilization of a periodic regular spiking regime. At the bifurcation point numerous regimes with nonequal interspike intervals emerge.