DYNAMICAL BEHAVIOR OF THE GENERALIZED COMPLEX LORENZ CHAOTIC SYSTEM |
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| Institution: | Chongqing Key Laboratory of Social Economy and Applied Statistics, School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China,Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada |
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| Abstract: | The purpose of this paper is to investigate the boundedness and global attractivity of
the complex Lorenz system:
x y x ? ? ? ? ?, y x cy dxz ? ? ? ? , ? ?
1
,
2
z z xy xy ? ? ? ? ?
where
? ? ? , , , , c d
are real parameters,
x
and
y
are complex variables,
z
is a real
variable, an overbar denotes complex conjugate variable and dots represent
derivatives with respect to time. This system arises in many important applications in
laser physics and rotating fluids dynamics. It is very interesting that we find that this
system exhibits chaos phenomenon for the given parameters. Using generalized
Lyapunov-like functions, we prove the existence of the ultimate bound set and the
globally exponentially attractive set in this generalized complex Lorenz system. The
rate of the trajectories is also obtained. Numerical simulations show the effectiveness
and correctness of the conclusions. Finally, we present an application of our results
that obtained in this paper. |
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| Keywords: | Complex Lorenz chaotic system chaotic attractor Lyapunov exponent Lyapunov dimension global attractivity |
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