1,426 research outputs found
Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities
In this paper we consider instabilities of localised solutions in planar neural field firing rate models of Wilson-Cowan or Amari type. Importantly we show that angular perturbations can destabilise spatially localised solutions. For a scalar model with Heaviside firing rate function we calculate symmetric one-bump and ring solutions explicitly and use an Evans function approach to predict the point of instability and the shapes of the dominant growing modes. Our predictions are shown to be in excellent agreement with direct numerical simulations. Moreover, beyond the instability our simulations demonstrate the emergence of multi-bump and labyrinthine patterns.
With the addition of spike-frequency adaptation, numerical simulations of the resulting vector model show that it is possible for structures without rotational symmetry, and in particular multi-bumps, to undergo an instability to a rotating wave. We use a general argument, valid for smooth firing rate functions, to establish the conditions necessary to generate such a rotational instability. Numerical continuation of the rotating wave is used to quantify the emergent angular velocity as a bifurcation parameter is varied. Wave stability is found via the numerical evaluation of an associated eigenvalue problem
Dynamical Synapses Enhance Neural Information Processing: Gracefulness, Accuracy and Mobility
Experimental data have revealed that neuronal connection efficacy exhibits
two forms of short-term plasticity, namely, short-term depression (STD) and
short-term facilitation (STF). They have time constants residing between fast
neural signaling and rapid learning, and may serve as substrates for neural
systems manipulating temporal information on relevant time scales. The present
study investigates the impact of STD and STF on the dynamics of continuous
attractor neural networks (CANNs) and their potential roles in neural
information processing. We find that STD endows the network with slow-decaying
plateau behaviors-the network that is initially being stimulated to an active
state decays to a silent state very slowly on the time scale of STD rather than
on the time scale of neural signaling. This provides a mechanism for neural
systems to hold sensory memory easily and shut off persistent activities
gracefully. With STF, we find that the network can hold a memory trace of
external inputs in the facilitated neuronal interactions, which provides a way
to stabilize the network response to noisy inputs, leading to improved accuracy
in population decoding. Furthermore, we find that STD increases the mobility of
the network states. The increased mobility enhances the tracking performance of
the network in response to time-varying stimuli, leading to anticipative neural
responses. In general, we find that STD and STP tend to have opposite effects
on network dynamics and complementary computational advantages, suggesting that
the brain may employ a strategy of weighting them differentially depending on
the computational purpose.Comment: 40 pages, 17 figure
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