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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

A New 4-D Chaotic Hyperjerk System with One Stable Equilibrium: Multistability, Hopf Bifurcation Analysis and Application to Pseudorandom Bit Generator

Discontinuity, Nonlinearity, and Complexity 15(1) (2026) 23--35 | DOI:10.5890/DNC.2026.03.003

Savvas Kosmidis, Efthymia Meletlidou, Christos Volos

Physics Department, Aristotle University of Thessaloniki, GR-54124 Thessaloniki, Greece

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Abstract

In this paper, a novel 4-D hyperjerk system with one stable equilibrium at the origin is presented. The system is constructed via a specific procedure and the stability of the equilibrium is determined by Routh-Hurwitz criterion. Numerical investigation of the system by using the bifurcation diagram, phase portraits, Lyapunov exponents and basins of attractions uncovers its chaotic dynamics and multistability. Also, the projection method of Kuznetzov is followed in order to study the Hopf bifurcation of the system. In addition, a pseudorandom bit generator is introduced. The pseudorandom bit sequence is generated by a chaotic solution of the system and the randomness of the bitstream is confirmed by NIST 800-22.

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