Differential Transform Method as an Effective Tool for Investigating Fractional Dynamical Systems

This study investigates the use of the differential transform method (DTM) for integrating the Rössler system of the fractional order. Preliminary studies of the integer-order Rössler system, with reference to other well-established integration methods, made it possible to assess the quality of the method and to determine optimal parameter values that should be used when integrating a system with different dynamic characteristics. Bifurcation diagrams obtained for the Rössler fractional system show that, compared to the RK4 scheme-based integration, the DTM results are more resistant to changes in the fractionality of the system.

Generating a New Chaotic System Using Two Chaotic Rossler-Chua Coupling Systems

It is proposed in this paper that a new chaotic system may be formed by combining two distinct chaotic systems, such as the Rossler system and the Chua system, in which the x dynamic of the Rossler system is linked with the z dynamic of the Chua system, results in a new chaotic system. Some of the basic dynamic behavior is explored and examined for new system by using the Matlab program. They noticed that it was a difference in the time series of the Chua system and this in turn led to a difference in the attractor, as the attractor of the Chua system changed from double scroll to single scroll and this led to change of the bandwidth of the Chua system, meaning that the Rӧssler system affected the Chua system, which led to an increase in the possibility of using this system in secret communications.

Controlling Bifurcation in Electronic Implementation of Dynamical Systems

In the theoretical and experimental studies of bifurcations in dynamical systems, the adjustments of the parameter values play a key role. The reason is because small variations in these values may result in topological changes in the behavior of the flow of the system. Taking this into account, in this paper, a new design for controlling bifurcation, suitable for electronic implementations of chaotic systems, is presented. The variation of the bifurcation parameter is performed by means of an Arduino UNO micro-controller and a digital controlled potentiometer. In this way, the variation of the electronic components is performed in an automated manner, avoiding the intrinsic problems of a manual variation of the circuit parameters. As a particular example, a scaled Rössler system is considered. One of the advantages of the controlled automated bifurcation is that it is useful for analyzing the robustness of the different limiting behaviors of the system against parameter mismatches.