The complex Lorenz equations
نویسندگان
چکیده
منابع مشابه
The Complex Lorenz Equations
where x and y ace co~aplex and z is real. The complex parameters r and a are defined by r = rl + it,,: a = 1 ie and o" and b are real. Behaviour ~markab ly different from the real Lo~,~nz model occurs. Only the origin is a fixed point except for the ~pecial case e + ~ = 0. We have been able to determine analytically two critical values of rt, namely r~ and rb. The or ion is a stable fixed point...
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We demonstrate that a system obeying the complex Lorenz equations in the deep chaotic regime can be controlled to periodic behavior by applying a modulation to the pump parameter. For arbitrary modulation frequency and amplitude there is no obvious simplification of the dynamics. However, we find that there are numerous windows where the chaotic system has been controlled to different periodic ...
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1. Much of the recent literature on chaos in dynamtransitions can be intermittent. ical systems has been concerned with pointing out the All these phenomena, and particularly hysteresis, behavioural similarity of many different types of can be explained on the basis of a suitable non-monomodels. The transition to aperiodic motion via the tone difference equation [11], such as that relating (Fei...
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Article history: Received 15 August 2015 Accepted 28 September 2015 Available online 3 October 2015 Communicated by F. Porcelli
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We announce and outline a proof of the existence of a homoclinic orbit of the Lorenz equations. In addition, we develop a shooting technique and two key conditions, which lead to the existence of a one-to-one correspondence between a set of solutions and the set of all infinite sequences of l's and 3's.
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ژورنال
عنوان ژورنال: Physica D: Nonlinear Phenomena
سال: 1982
ISSN: 0167-2789
DOI: 10.1016/0167-2789(82)90057-4