Abstract
Dynamical degradation is a known problem in the computer simulation of chaotic systems. Data type limitations, sampling, and rounding errors give rise to the periodic behavior. In applications of chaotic systems in secure communication and cryptography systems, such effects can reduce data storage security and operation. In this study, we considered a possible solution to this problem by using semi-explicit integration. The key idea is to perturb the chaotic trajectory by switching between two integrators, which possess close but still different numerical solutions. Compared with the traditional approach based on the perturbation of the bifurcation parameter, this technique does not significantly change the nonlinear properties of the system. We verify the efficiency of the proposed perturbation method through several numerical experiments using the well-known Rössler oscillator.
Highlights
Chaotic systems have been widely used in many engineering and scientific tasks, including secure communication [1,2,3,4], neural networks [5,6], watermarking [7], cryptography [8,9,10], robotics [11,12], sensors [13], signal processing [14], etc
In addition to the identification error of the mathematical model, the discrepancy between the numerical results and the prototype behavior is enhanced by the data type precision, discretization methods error, and round-off results of arithmetic operations [15]
Thisphenomenon phenomenoncan canbe beexplained explainedasasfollows: follows:slight slightchanges changesinin the truncation errors and round-off errors of arithmetic operations result in simultaneous the truncation errors and round-off errors of arithmetic operations result in simultaneous changes changesin inthe thediscrete discretesystem’s system’strajectory
Summary
Chaotic systems have been widely used in many engineering and scientific tasks, including secure communication [1,2,3,4], neural networks [5,6], watermarking [7], cryptography [8,9,10], robotics [11,12], sensors [13], signal processing [14], etc. The study of chimera states in ensembles of coupled oscillators implies long-term simulation [30] In both cases, the considered techniques for avoiding dynamical degradation can distort the results of the analysis. The considered techniques for avoiding dynamical degradation can distort the results of the analysis Such methods are not applicable for synchronization-based communication systems since any perturbation violates the identity of the oscillations generated by the receiver and transmitter. The new technique for extending the period of chaotic sequences is given; the proposed method does not introduce additional perturbations to the chaotic oscillations in comparison with traditional methods based on switching nonlinearity parameters; the considered approach can be implemented in embedded systems without using additional hardware resources.
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