Stable finite difference method for fractional reaction–diffusion equations by compact implicit integration factor methods

In this paper we propose a stable finite difference method to solve the fractional reaction–diffusion systems in a two-dimensional domain. The space discretization is implemented by the weighted shifted Grünwald difference (WSGD) which results in a stiff system of nonlinear ordinary differential equations (ODEs). This system of ordinary differential equations is solved by an efficient compact implicit integration factor (cIIF) method. The stability of the second order cIIF scheme is proved in the discrete $L^{2}$ L 2 -norm. We also prove the second-order convergence of the proposed scheme. Numerical examples are given to demonstrate the accuracy, efficiency, and robustness of the method.

Chaotic Communication System with Symmetry-Based Modulation

Communication systems based on chaotic synchronization are gaining interest in the area of secure and covert data transmission. In this paper, a novel digital communication technique based on a coherent chaotic data transmission approach is proposed. In general, this technique resembles the well-known approach based on the modulation of nonlinearity parameters. The key idea of this study is to modulate a signal by varying not the system parameter but the symmetry coefficient in discrete chaotic models obtained by the special numerical integration method. For this purpose, the self-adjoint semi-implicit integration method of order 2 is used to obtain discrete master and slave models of the considered chaotic oscillator. The experimental results explicitly show that, like during parameter modulation, transmitting and receiving oscillators may completely synchronize only if the symmetry coefficients are equal in both systems. The architecture of the communication system based on the proposed modulation is presented. The practical applicability of the approach is confirmed by transmitting a test binary sequence between the transmitter and receiver models and preliminary benchmarking of the obtained communication system. Since the symmetry coefficient modulation does not significantly impact the chaotic behavior of the transmitting digital system, its better suitability for covert messaging was experimentally confirmed by comparing it with the parameter modulation technique.