https://doi.org/10.1140/epjp/s13360-023-04504-1
Regular Article
n-dimensional polynomial hyperchaotic systems with synchronization application
Electronic Engineering College, Heilongjiang University, 150080, Harbin, China
Received:
8
August
2023
Accepted:
18
September
2023
Published online:
15
October
2023
Most existing chaotic maps have many defects in engineering applications, such as discontinuous parameter range, weak chaos, uneven output of chaotic sequences and dynamic degradation. Based on this, a generalized n-dimensional polynomial chaotic map is proposed in this paper. By setting the coefficient of the linear term and the order of the highest order term of the polynomial, a series of n-dimensional polynomial hyperchaotic maps of specific Lyapunov exponents can be obtained. One can get the desired number of positive Lyapunov exponents, and one can get the desired value of positive Lyapunov exponents. Then, the P–M synchronization based on the n-dimensional polynomial hyperchaotic maps is also proposed. By constructing an invertible matrix P, any matrix M, and choosing a matrix F such that the eigenvalues of the matrix 
are placed strictly inside the unit disk, the master and slave systems can be synchronized. Numerical experiments also show the feasibility of this scheme.
The authors Wenhao Yan and Qun Dingy have contributed equally to this work.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
