A Chaotic oscillations in a new 2-D discrete dynamical system with hidden parameter
A new 2-D chaotic discrete dynamical system with hidden parameter
Abstract
The main purpose of this work is the presentation of a new 2-D chaotic discrete dynamical system. Based on the study of their basic properties, such as the determination of their fixed points, then their type of stability according to the values of the bifurcation parameters, and by using the Lyapunov exponents, we obtain chaotic oscillations for certain values of a whatever the value of the second parameter b, which implies that its value has no effect on the dynamic of the system, and make it more distinctive, it will be called later the hidden parameter.
The discovered system which will be noted by B_{a,b}, has many useful characteristics, in particular, its quadratic form, the differentiability of its corresponding function, and more still, the non-appearance of the parameter b in their eigenvalues, and that its choice will be arbitrary, furthermore facilitated the calculs. Simulation work validates all thoughts towards chaotic behavior.
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References
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