Formation of defects in network under local energy balance

Continuous oscillation in nonlinear circuits relies on stable exchange and propagation of field energy between different branch circuits. When the dynamics of these nonlinear circuits are defined by nonlinear oscillators, an equivalent Hamilton energy function is considered as sole Lyapunov function and can be used to predict the attractor stability and transition in oscillatory states. Excessive energy accumulation may induce rapid shift of physical parameter for electric component and similar shape deformation in biological tissue. In this paper, Rössler oscillators are connected in a square network by activating adjacent neighbor coupling, the local energy function is obtained by using Helmholtz theorem, and local energy diversity between adjacent oscillators can induce one parameter shift until reaching adaptive energy balance. As a result, energy diversity supports the formation of defects and some identical oscillators become non-identical for reaching phase lock in the network on square array. In the presence of noisy disturbance, energy diversity becomes available and parameter shift is induced to create defects in the network for reaching local energy balance.