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Chaotic phenomenon has a good ability to search for §an optimal solution of a problem with many local §minima. The current work uses the chaos theory with§focus on electrical circuits. Chua s circuit is a §good example to demonstrate the type of non-§linearity in the electrical circuit which causes §chaos.The opamp based hysteresis neuron model is §implemented and its stability is explained. §Stability criterion of the network can be used as a §cost function and when the network reaches its §stable point, this corresponds to a solution. This is§explained in regards to N-queens problem.The circuit §topology for solving 8-queens problem is proposed §that can be extended to N-queens.The hysteresis §neuron model is implemented using the double gate §MOSFET. Once we are able to build this analog §circuit representation of the network, the solution §can be obtained in a constant time irrespective of §the network size.