Related papers: Structural Characterization of Oscillations in Bra…
Propagation of oscillatory signals through the cortex and coherence is shaped by the connectivity structure of neuronal circuits. This study systematically investigates the network and stimulus properties that shape network responses. The…
Recently, self-sustained oscillations in complex networks consisting of nonoscillatory nodes (network oscillators) have attracted great interest in diverse natural and social fields. Due to complexity of network behaviors, little is known…
The paper examines the discrete-time dynamics of neuron models (of excitatory and inhibitory types) with piecewise linear activation functions, which are connected in a network. The properties of a pair of neurons (one excitatory and the…
Functional oscillator networks, such as neuronal networks in the brain, exhibit switching between metastable states involving many oscillators. We give exact results how such global dynamics can arise in paradigmatic phase oscillator…
Network theory is rapidly changing our understanding of complex systems, but the relevance of topological features for the dynamic behavior of metabolic networks, food webs, production systems, information networks, or cascade failures of…
Inhibitory neurons play a crucial role in maintaining persistent neuronal activity. Although connected extensively through electrical synapses (gap-junctions), these neurons also exhibit interactions through chemical synapses in certain…
Low-dimensional yet rich dynamics often emerge in the brain. Examples include oscillations and chaotic dynamics during sleep, epilepsy, and voluntary movement. However, a general mechanism for the emergence of low dimensional dynamics…
Most complex systems are nonlinear, relying on emergent behavior from interacting subsystems, often characterized by oscillatory dynamics. Collective oscillatory behavior is essential for the proper functioning of many real world systems.…
Cortical neurons emit seemingly erratic trains of action potentials or "spikes," and neural network dynamics emerge from the coordinated spiking activity within neural circuits. These rich dynamics manifest themselves in a variety of…
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…
Recent experiments have highlighted how collective dynamics in networks of brain regions affect behavior and cognitive function. In this paper we show that a simple, homogeneous system of densely connected oscillators representing the…
We continue the work of a series of previous studies of a mathematical model that describes the mean-field limit behavior of a homogeneous network of excitatory point spiking neurons. Contrary to other models, here noise is intrinsic to the…
We propose a stochastic dynamical model of noisy neural networks with complex architectures and discuss activation of neural networks by a stimulus, pacemakers and spontaneous activity. This model has a complex phase diagram with…
We analyse mathematical models in order to understand how microstructural features of vascular networks may affect blood-flow dynamics, and to identify particular characteristics that promote the onset of self-sustained oscillations. By…
There is enormous interest -- both mathematically and in diverse applications -- in understanding the dynamics of coupled oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology,…
Neural oscillations are considered to be brain-specific signatures of information processing and communication in the brain. They also reflect pathological brain activity in neurological disorders, thus offering a basis for diagnoses and…
Starting from the morphological-functional assumption of the fractal brain, a mathematical model is given by activating brain non-differentiable dynamics through the determinism-nondeterminism inference of the responsible mechanisms. The…
At the macroscale, the brain operates as a network of interconnected neuronal populations, which display rhythmic dynamics that support interareal communication. Understanding how stimulation of a particular brain area impacts such…
We utilize a model of Wilson-Cowan oscillators to investigate structure-function relationships in the human brain by means of simulations of the spontaneous dynamics of brain networks generated through human connectome data. This allows us…
The mammalian brain could contain dense and sparse network connectivity structures, including both excitatory and inhibitory neurons, but is without any clearly defined output layer. The neurons have time constants, which mean that the…