Oscillations in Discrete and Continuous Hoppeld Networks
نویسندگان
چکیده
This chapter is neatly partitioned into two parts: one dealing with oscillations in discrete Hoppeld networks and the other with oscillations in continuous Hoppeld networks. The single theme spanning both parts is that of the Hoppeld model and its energy function. The rst part deals with analyzing oscillations in the discrete Hoppeld network with symmetric weights, and speculating on possible uses of such behavior. By imposing certain restrictions on the weights, an exact characterization of the oscillatory behavior is obtained. Possible uses of this characterization are examined. The second part deals with injecting chaotic or periodic oscillations into continuous Hoppeld networks, for the purposes of solving optimization problems. When the continuous Hoppeld model is used to solve an optimization problem, the results are often mediocre because of the convergent nature of its dynamical algorithm. To circumvent this limitation, we develop mechanisms for injecting controllable chaos or periodic oscillations into the Hoppeld network. We allow chaotic or oscillatory behavior to be initiated, and converted to convergent behavior, at the turn of a \knob", in rough analogy with simulated annealing. The resulting algorithm, called chaotic annealing, is evaluated on instances of Maximum Clique|an NP-hard optimization problem on graphs|and shown to exhibit a signiicant improvement over the convergent Hoppeld dynamics.
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