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Deep artificial neural networks have surpassed human-level performance across a diverse array of complex learning tasks, establishing themselves as indispensable tools in both social applications and scientific research. Despite these…
Spiking Neural Networks (SNNs) emulate the integrated-fire-leak mechanism found in biological neurons, offering a compelling combination of biological realism and energy efficiency. In recent years, they have gained considerable research…
Many experimental results, both in-vivo and in-vitro, support the idea that the brain cortex operates near a critical point, and at the same time works as a reservoir of precise spatio-temporal patterns. However the mechanism at the basis…
This work concerns the long-term dynamics of a spatiotemporal many-body deterministic model that exhibits emergence and self-organization, and which has been recently proposed as a new paradigm for Artificial Life. Collective structures…
We consider a large network of Izhikevich neurons. Each neuron has a quadratic integrate-and-fire type model with a recovery variable modelling spike frequency adaptation (SFA). We introduce a biologically motivated synaptic current…
We analyze states of stationary activity in randomly coupled quadratic integrate-and-fire neurons using stochastic mean-field theory. Specifically, we consider the two cases of Gaussian random coupling and Cauchy random coupling, which are…
The state space of a conventional Hopfield network typically exhibits many different attractors of which only a small subset satisfy constraints between neurons in a globally optimal fashion. It has recently been demonstrated that combining…
Recurrent networks of dynamic elements frequently exhibit emergent collective oscillations, which can display substantial regularity even when the individual elements are considerably noisy. How noise-induced dynamics at the local level…
We revisit the dynamics of a prototypical model of balanced activity in networks of spiking neutrons. A detailed investigation of the thermodynamic limit for fixed density of connections (massive coupling) shows that, when inhibition…
Intrinsic stochasticity can induce highly non-trivial effects on dynamical systems, including stochastic and coherence resonance, noise induced bistability, noise-induced oscillations, to name but a few. In this paper we revisit a mechanism…
Neurons and networks in the cerebral cortex must operate reliably despite multiple sources of noise. To evaluate the impact of both input and output noise, we determine the robustness of single-neuron stimulus selective responses, as well…
We show that a network of spiking neurons exhibits robust self-organized criticality if the synaptic efficacies follow realistic dynamics. Deriving analytical expressions for the average coupling strengths and inter-spike intervals, we…
In many stochastic dynamical systems, ordinary chaotic behavior is preceded by a full-dimensional phase that exhibits 1/f-type power-spectra and/or scale-free statistics of (anti)instantons such as neuroavalanches, earthquakes, etc. In…
We consider a heterogeneous, globally coupled population of excitatory quadratic integrate-and-fire neurons with excitability adaptation due to a metabolic feedback associated with ketogenic diet, a form of therapy for epilepsy. Bifurcation…
We analyze the dynamics of networks of spiking neural oscillators. First, we present an exact linear stability theory of the synchronous state for networks of arbitrary connectivity. For general neuron rise functions, stability is…
In this work, we study the dynamic range of a neuronal network of excitable neurons with excitatory and inhibitory synapses. We obtain an analytical expression for the critical point as a function of the excitatory and inhibitory synaptic…
Previous work showed that the collective activity of large neuronal networks can be tamed to remain near its critical point by a feedback control that maximizes the temporal correlations of the mean-field fluctuations. Since such…
We propose a neural network model with transient chaos, or a transiently chaotic neural network (TCNN) as an approximation method for combinatorial optimization problem, by introducing transiently chaotic dynamics into neural networks.…
We study a stochastic system of interacting neurons and its metastable properties. The system consists of $N$ neurons, each spiking randomly with rate depending on its membrane potential. At its spiking time, the neuron potential is reset…
Synchronized oscillations in networks of inhibitory and excitatory coupled bursting neurons are common in a variety of neural systems from central pattern generators to human brain circuits. One example of the latter is the subcortical…