Abstract
Objectives: This paper introduces a novel 4D autonomous dynamic system with five line equilibria and a smooth nonlinearity. Methods/ statistical analysis: The new model is obtained by adding one more freedom degree to the 3D jerk system recently introduced by Kengne and Mogue, 2018. To analyze and study the model, Ruth criterion principle is used for the stability of different lines equilibria. Using traditional dynamics tools such as bifurcation diagrams, phase portraits, Poincare section, power spectrum, and Pspice software, the dynamic of the system is carried out. Findings: The new elegant system has an extremely rich dynamics predominated by the phenomenon of extreme multistability. The various sequences of coexisting route to chaos (coexisting bifurcation) confirm the uncertain destination of our novel elegant system. Note that, for the best of author’s knowledge, this is one of the best reproducible extreme multistable system because is not a flux control memristor-based system. Application/improvements: The results obtained in this investigation enrich the literature and being used to improve the extreme multistability application in many research domains such as Random Number Generation (RNG) and image encryption. Keywords: Five line equilibria, Extreme multistability, Composite tanh-cubic nonlinearity, PSpice simulations.
Highlights
In recent years, multistability has been the subject of several research projects [1,2,3,4,5,6,7,8]
Multistability has been the subject of several research projects [1,2,3,4,5,6,7,8]. This complex feature of chaotic systems started attracting scientists’ attention in 1986 [9,10]. It is mainly characterized by its extreme sensitivity to initial conditions and noises
A question comes to our mind: how to get a chaotic oscillator so that the dynamics is extremely sensitive to the initial conditions? Before going into the work proper, let’s recall a few words the previous works whose focus was on extreme multistability
Summary
Multistability has been the subject of several research projects [1,2,3,4,5,6,7,8]. Only the infinity of solution allows limiting the higher number of coexisting attractors for a given model After this analysis, a question comes to our mind: how to get a chaotic oscillator so that the dynamics is extremely sensitive to the initial conditions? We obtained a new 4D autonomous chaotic dynamic system with extreme multistability, where the circuit implementation is achieved without any memristor simulator or emulator. This new elegant extreme multistable system presents certain irrefutable advantages over other systems: firstly, it has a smooth nonlinear function; secondly, it offers up to five line equilibria presented, and thirdly, the system exhibits the phenomenon of extreme multistability. Conclusion and remarks of our contribution constitute section 5
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