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Dynamics of one dimensional mouse map. (English) Zbl 1475.37040

Summary: In this paper, we have discussed the dynamics of 1-D Mouse map which is also known as Gaussian Iterated map or simply Gauss map and analyzed their chaotic behaviors in several senses. We have mainly focused on several chaotic dynamics like Orbit Analysis, Time Series Analysis, Lyapunov Exponent Analysis, Sensitivity to Initial Conditions, Bifurcation Diagram, Cobweb Diagram, Histogram, Trajectories and Sensitivity to Numerical Inaccuracies of this map. Finally we have shown its graphical analysis and found that this map is chaotic in the mentioned senses. We have performed all graphical activities by using Mathematica and MATLAB.

MSC:

37E05 Dynamical systems involving maps of the interval
37G10 Bifurcations of singular points in dynamical systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37M20 Computational methods for bifurcation problems in dynamical systems

Software:

Mathematica
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Full Text: Link

References:

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