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Synchronization and desynchronization are the two ends on the spectrum of emergent phenomena that somehow often coexist in biological, neuronal, and physical networks. However, previous studies essentially regard their coexistence as a…
The dynamics of a neural model for hippocampal place cells storing spatial maps is studied. In the absence of external input, depending on the number of cells and on the values of control parameters (number of environments stored, level of…
Complex diseases can be modeled as damage to intracellular networks that results in abnormal cell behaviors. Network-based dynamic models such as Boolean models have been employed to model a variety of biological systems including those…
Inhibition is considered to shape neural activity, and broaden its pattern repertoire. In the sensory organs, where the anatomy of neural circuits is highly structured, lateral inhibition sharpens contrast among stimulus properties. The…
We introduce and analyze a class of neural network models motivated by the Drosophila central complex nervous system, designed to capture the emergence and dynamics of orientation-selective activity bumps. Starting from a biologically…
Systems with the coexistence of different stable attractors are widely exploited in systems biology in order to suitably model the differentiating processes arising in living cells. In order to describe genetic regulatory networks several…
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…
In the classic view of cortical rhythms, the interaction between excitatory pyramidal neurons (E) and inhibitory parvalbumin neurons (I) has been shown to be sufficient to generate gamma and beta band rhythms. However, it is now clear that…
Many experiments have evidenced that electrical and chemical synapses -- hybrid synapses -- coexist in most organisms and brain structures. The role of electrical and chemical synapse connection in diversity of neural activity generation…
We study networks of theta neurons arranged on a ring with delayed interactions. In the continuum limit the systems are described by next generation neural field models with delays. We consider distributed delays with both finite and…
The attractors of a dynamical system govern its typical long-term behaviour. The presence of many attractors is significant as it means the behaviour is heavily dependent on the initial conditions. To understand how large numbers of…
Contemporary modeling approaches to the dynamics of neural networks consider two main classes of models: biologically grounded spiking neurons and functionally inspired rate-based units. The unified simulation framework presented here…
This paper presents a stability analysis of simple neuromodules displaying fold bifurcations (leading to hysteresis), flip bifurcations (period doubling and undoubling to and from chaos) and Neimark-Sacker bifurcations (quasiperiodic and…
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…
Oscillations are a hallmark of neural population activity in various brain regions with a spectrum covering a wide range of frequencies. Within this spectrum gamma oscillations have received particular attention due to their ubiquitous…
Boolean Networks (BNs) describe the time evolution of binary states using logic functions on the nodes of a network. They are fundamental models for complex discrete dynamical systems, with applications in various areas of science and…
We analyze a class of network motifs in which a short, two-node positive feed- back motif is inserted in a three-node negative feedback loop. We demonstrate that such networks can undergo a bifurcation to a state where a stable fixed point…
We study synaptically coupled neuronal networks to identify the role of coupling delays in network's synchronized behaviors. We consider a network of excitable, relaxation oscillator neurons where two distinct populations, one excitatory…
We demonstrate neuron-like spiking dynamics in the asymmetrically driven dissipative photonic Bose-Hubbard dimmer model which describes two coupled nonlinear passive Kerr cavities. Spiking dynamics appear due to the excitable nature of the…
We study the joint dynamics of membrane potential and time since the last spike in a population of integrate-and-fire neurons using a population density framework. This leads to a two-dimensional Fokker-Planck equation that captures the…