Continuous attractor neural networks (CANNs) are models that describe neuronal systems having localized activities to represent continuous information. Head-direction (HD) cells, place cells and orientation selective cells in the primary visual cortex are examples. In a CANN, due to the localized excitatory couplings, tuning curves of neurons are bump-shaped functions of external stimuli. The particular stimulus that the activity of a neuron is maximized is the preferred stimulus of that neuron. As a result, the neuronal activities in a CANN are also bump-shaped functions of the preferred stimulus of the neurons. If the synapses (the couplings between neurons) in a CANN are static, the neuronal activity profile will also be stable. However, if the synapses are dynamical, the neuro...[ Read more ]

Continuous attractor neural networks (CANNs) are models that describe neuronal systems having localized activities to represent continuous information. Head-direction (HD) cells, place cells and orientation selective cells in the primary visual cortex are examples. In a CANN, due to the localized excitatory couplings, tuning curves of neurons are bump-shaped functions of external stimuli. The particular stimulus that the activity of a neuron is maximized is the preferred stimulus of that neuron. As a result, the neuronal activities in a CANN are also bump-shaped functions of the preferred stimulus of the neurons. If the synapses (the couplings between neurons) in a CANN are static, the neuronal activity profile will also be stable. However, if the synapses are dynamical, the neuronal activity profile may be unstable. There are two possibilities that make synapses dynamical. Short-term synaptic depression (STD) is an effect that can temporally degrade the synaptic efficacy due to the recent firing history of the presynaptic neuron. This is due to the fact that the recovery time of neurotransmitters (~100 ms) is longer than the time scale of synaptic current (~1 ms). STD can destabilize the bump-shaped states in CANNs. Several contributions are reported in this thesis. First, I report that STD enables the CANN to support plateau states, which can be a mechanism of sensory memory. Also, STD can translationally destabilize states in CANNs. This translational instability enables the CANN to implement anticipation as a mechanism of delay compensation in the nervous system, which was also observed in rodent experiments. The novelty of the proposed mechanism is based on the inherent and ubiquitous nature of STD of neurons, and does not require dedicated neuronal mechanisms and network structures as was the case in previous models. Second, under the influence of external inputs and STD, there are periodic excitements of the neuronal activity. We found that the resolution of CANNs can be improved significantly due to the periodic excitements. Also, the simulation results are comparable to psychology experiments and neuroscience experiments. This suggests a novel way to encode multiple almost-overlapped stimuli. Third, I studied Short-term synaptic facilitation (STF) an effect that can temporally enhance the synaptic efficacy. This effect is due to the rise of calcium level in the presynaptic neuron after a spike. STF can stabilize the network states. It can be used to reduce the effect of noisy stimuli. Fourth, apart from the study of one-dimensional (1D) CANN, in the thesis, I also present the study on the intrinsic dynamics of two-dimensional (2D) CANN with STD and local subtractive inhibition.