The Lyapunov exponents and Poincaré maps of nonlinear chaotic characteristic in three-cell coupled quantum cellular neural networks

With the polarization of quantum-dot cell and quantum phase serving as state variables, both theoretical analysis and simulation are made of the complex chaotic dynamical behavior of a three-cell-coupled Quantum Cellular Neural Network, including equilibrium points, Lyapunov exponents and Poincare maps. As a result, equilibrium points are obtained and found to be symmetric and periodic; three of the six Lyapunov exponents are found positive; the Poincare maps composed of a large number of thick dots which are distributed over a certain curve. The latter two items prove the chaotic behavior of this system.