This paper proposes a new spatiotemporal chaos model, which is a logistic-dynamic coupled logistic map lattice (LDCML). Through a large number of simulation experiments and theoretical analysis, it can be proved that a chaotic region has the larger parameter space, and the system is more chaotic compared with traditional CML by the introduction of a dynamic coupled method, which is more suitable for chaotic encryption and secure communications. So, this paper presents a bit-level adaptive image encryption algorithm based on this system, and further demonstrates the good chaos of the system from the aspect of encryption performance.

To reduce parameter error caused by human factors and ensure the accuracy of the largest Lyapunov exponent (LLE) obtained from chaotic equations, this paper proposes a simple method based on two nearby pseudo-orbits. First, a point is selected from a solution trajectory of chaotic equation by the roundoff error. Second, the selected point is used as an initial condition to solve the same equation to obtain another solution trajectory. Third, the evolution distance of the two solution trajectories is calculated. Finally, the LLE is the slope of the linear region in the curve of the track distance of the natural algorithm. Our method has been successfully applied to simulate five well-known chaotic systems and some non-chaotic systems. The results show that, compared with other traditional methods, the proposed method is efficient, simple, and robust without reconstructing phase space and computing the Jacobian matrix.

In this paper, the problem of synchronization for a class of fully complex-valued networks with coupling delay is investigated by the linear feedback control in a finite time. The state variables, system function, inner coupling matrix, and outer coupling matrix in this model are set as complex values. By decomposing the complex-valued network into real and imaginary parts, an equivalent real-valued system is established. Based on the finite-time stability theory and Lyapunov functional method, linear feedback controllers are constructed to guarantee the synchronization for the complex-valued networks with or without coupling delay in a desired finite time. Then, some sufficient conditions for assurance of finite-time synchronization are given by strict proof. Finally, simulation examples are provided to verify our results.