We show analytically how the stability of two-dimensional lateral inhibition neural networks depends on the local connection topology. For various network topologies, we calculate the critical time delay for the onset of oscillation in continuous-time networks and present analytic phase diagrams characterizing the dynamics of discrete-time networks.

We show analytically how the stability of two-dimensional lateral inhibition neural networks depends on the local connection topology. For various network topologies, we calculate the critical time delay for the onset of oscillation in continuous-time networks and present analytic phase diagrams characterizing the dynamics of discrete-time networks.

We show analytically how the stability of two-dimensional lateral inhibition neural networks depends on the local connection topology. For various network topologies, we calculate the critical time delay for the onset of oscillation in continuous-time networks and present analytic phase diagrams characterizing the dynamics of discrete-time networks.

A time delay in the response of the neurons in a network can induce sustained oscillation and chaos. We present a stability criterion based on local stability analysis to prevent sustained oscillation in symmetric delay networks, and show an example of chaotic dynamics in a non-symmetric delay network.

A time delay in the response of the neurons in a network can induce sustained oscillation and chaos. We present a stability criterion based on local stability analysis to prevent sustained oscillation in symmetric delay networks, and show an example of chaotic dynamics in a non-symmetric delay network.

A time delay in the response of the neurons in a network can induce sustained oscillation and chaos. We present a stability criterion based on local stability analysis to prevent sustained oscillation in symmetric delay networks, and show an example of chaotic dynamics in a non-symmetric delay network.