Theory of stability in a nonlinear resistive network

In a nonlinear resistive network, Kirchhoff's laws and branch equations generally give several solutions as operating points. We have studied the condition of the stability of the solutions, taking into account the curvature of the total power in voltage-current space. Since the power of each element is expressed by integration over the voltage and current as independent functions, this new expression makes a geometrical representation of the total power. It is shown that the differentiable and minimum points correspond to the physical operating points of the network.