A fundamental property of cortical neurons is the capacity to exhibit adaptive changes or plasticity. Whether adaptive changes in cortical responses are accompanied by changes in synchrony between individual neurons and local population activity in sensory cortex is unclear. This issue is important as synchronized neural activity is hypothesized to play an important role in propagating information in neuronal circuits. Here, we show that rapid adaptation (300 ms) to a stimulus of fixed orientation modulates the strength of oscillatory neuronal synchronization in macaque visual cortex (area V4) and influences the ability of neurons to distinguish small changes in stimulus orientation. Specifically, rapid adaptation increases the synchronization of individual neuronal responses with local population activity in the gamma frequency band (30 -80 Hz). In contrast to previous reports that gamma synchronization is associated with an increase in firing rates in V4, we found that the postadaptation increase in gamma synchronization is associated with a decrease in neuronal responses. The increase in gamma-band synchronization after adaptation is functionally significant as it is correlated with an improvement in neuronal orientation discrimination performance. Thus, adaptive synchronization between the spiking activity of individual neurons and their local population can enhance temporally insensitive, rate-based-coding schemes for sensory discrimination.

We consider the effect of the effective timing of a delayed feedback on the excitatory neuron in a recurrent inhibitory loop, when biological realities of firing and absolute refractory period are incorporated into a phenomenological spiking linear or quadratic integrate-and-fire neuron model. We show that such models are capable of generating a large number of asymptotically stable periodic solutions with predictable patterns of oscillations. We observe that the number of fixed points of the so-called phase resetting map coincides with the number of distinct periods of all stable periodic solutions rather than the number of stable patterns. We demonstrate how configurational information corresponding to these distinct periods can be explored to calculate and predict the number of stable patterns.

We consider a pair of stochastic integrate and fire neurons receiving correlated stochastic inputs. The evolution of this system can be described by the corresponding Fokker-Planck equation with non-trivial boundary conditions resulting from the refractory period and firing threshold. We propose a finite volume method that is orders of magnitude faster than the Monte Carlo methods traditionally used to model such systems. The resulting numerical approximations are proved to be accurate, nonnegative and integrate to 1. We also approximate the transient evolution of the system using an Ornstein-Uhlenbeck process, and use the result to examine the properties of the joint output of cell pairs. The results suggests that the joint output of a cell pair is most sensitive to changes in input variance, and less sensitive to changes in input mean and correlation.

Abstract. We study the coexistence of multiple periodic solutions for an analogue of the integrateand-fire neuron model of two-neuron recurrent inhibitory loops with delayed feedback, which incorporates the firing process and absolute refractory period. Upon receiving an excitatory signal from the excitatory neuron, the inhibitory neuron emits a spike with a pattern-related delay, in addition to the synaptic delay. We present a theoretical framework to view the inhibitory signal from the inhibitory neuron as a self-feedback of the excitatory neuron with this additional delay. Our analysis shows that the inhibitory feedbacks with firing and the absolute refractory period can generate four basic types of oscillations, and the complicated interaction among these basic oscillations leads to a large class of periodic patterns and the occurrence of multistability in the recurrent inhibitory loop. We also introduce the average time of convergence to a periodic pattern to determine which periodic patterns have the potential to be used for neural information transmission and cognition processing in the nervous system.

Neural networks with a non-monotonic activation function have been proposed to increase their capacity for memory storage and retrieval, but there is still a lack of rigorous mathematical analysis and detailed discussions of the impact of time lag. Here we consider a two-neuron recurrent network. We first show how supercritical pitchfork bifurcations and a saddle-node bifurcation lead to the coexistence of multiple stable equilibria (multistability) in the instantaneous updating network. We then study the effect of time delay on the local stability of these equilibria and show that four equilibria lose their stability at a certain critical value of time delay, and Hopf bifurcations of these equilibria occur simultaneously, leading to multiple coexisting periodic orbits. We apply centre manifold theory and normal form theory to determine the direction of these Hopf bifurcations and the stability of bifurcated periodic orbits. Numerical simulations show very interesting global patterns of periodic solutions as the time delay is varied. In particular, we observe that these four periodic solutions are glued together along the stable and unstable manifolds of saddle points to develop a butterfly structure through a complicated process of gluing bifurcations of periodic solutions.