Bifurcation analysis in a silicon neuron

International audienceIn this paper, we describe an analysis of the nonlinear dynamical phenomenon associated with a silicon neuron. Our silicon neuron integrates Hodgkin-Huxley (HH) model formalism, including the membrane voltage dependency of temporal dynamics. Analysis of the bifurcation conditions allow us to identify different regimes in the parameter space that are desirable for biasing our silicon neuron. This approach of studying bifurcations is useful because it is believed that computational properties of neurons are based on the bifurcations exhibited by these dynamical systems in response to some changing stimulus. We describe numerical simulations and measurements of the Hopf bifurcation which is characteristic of class 2 excitability in the HH model. We also show a phenomenon observed in biological neurons and termed excitation block. Hence, by showing that this silicon neuron has similar bifurcations to a certain class of biological neurons, we can claim that the silicon neuron can also perform similar computation

Dynamical laser spike processing

Novel materials and devices in photonics have the potential to revolutionize optical information processing, beyond conventional binary-logic approaches. Laser systems offer a rich repertoire of useful dynamical behaviors, including the excitable dynamics also found in the time-resolved "spiking" of neurons. Spiking reconciles the expressiveness and efficiency of analog processing with the robustness and scalability of digital processing. We demonstrate that graphene-coupled laser systems offer a unified low-level spike optical processing paradigm that goes well beyond previously studied laser dynamics. We show that this platform can simultaneously exhibit logic-level restoration, cascadability and input-output isolation---fundamental challenges in optical information processing. We also implement low-level spike-processing tasks that are critical for higher level processing: temporal pattern detection and stable recurrent memory. We study these properties in the context of a fiber laser system, but the addition of graphene leads to a number of advantages which stem from its unique properties, including high absorption and fast carrier relaxation. These could lead to significant speed and efficiency improvements in unconventional laser processing devices, and ongoing research on graphene microfabrication promises compatibility with integrated laser platforms.Comment: 13 pages, 7 figure

Noise-activated barrier crossing in multi-attractor spiking networks

Noise-activated transitions between coexisting attractors are investigated in a chaotic spiking network. At low noise level, attractor hopping consists of discrete bifurcation events that conserve the memory of initial conditions. When the escape probability becomes comparable to the intra-basin hopping probability, the lifetime of attractors is given by a detailed balance where the less coherent attractors act as a sink for the more coherent ones. In this regime, the escape probability follows an activation law allowing us to assign pseudo-activation energies to limit cycle attractors. These pseudo-energies introduce a useful metric for evaluating the resilience of biological rhythms to perturbations

Memory-induced Excitability in Optical Cavities

Neurons and other excitable systems can release energy suddenly given a small stimulus. Excitability has recently drawn increasing interest in optics, as it is key to realize all-optical artificial neurons enabling speed-of-light information processing. However, the realization of all-optical excitable units and networks remains challenging. Here we demonstrate how laser-driven optical cavities with memory in their nonlinear response can sustain excitability beyond the constraints of memoryless systems. First we demonstrate different classes of excitability and spiking, and their control in a single cavity with memory. This single-cavity excitability is limited to a narrow range of memory times commensurate with the linear dissipation time. To overcome this limitation, we explore coupled cavities with memory. We demonstrate that this system can exhibit excitability for arbitrarily long memory times, even when the inter-cavity coupling rate is smaller than the dissipation rate. Our coupled-cavity system also sustains spike trains -- a hallmark of neurons -- that spontaneously break mirror symmetry. Our predictions can be readily tested in thermo-optical cavities, where thermal dynamics effectively give memory to the nonlinear optical response. The huge separation between thermal and optical time scales in such cavities is promising for the realization of artificial neurons that can self-organize to the edge of a phase transition, like many biological systems do