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Abstract:
Because the dynamics of a neural network with symmetric
interactions is similar t to a gradient descent dynamics,
convergence to a fixed point is the general behavior. In this
paper, we analyze the global behavior of networks with distinct
excitatory and inhibitory populations of neurons, under the
assumption that the interactions between the populations are
antisymmetric. Our analysis exploits the similarity of such a
dynamics to a saddle point dynamics. This analogy gives some
intuition as to why such a dynamics can either converge to a fixed
point or a limit cycle, depending on parameters. We also show that
the network dynamics can be written in a dissipative Hamiltonian
form.
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