منابع مشابه
Symbolic dynamics analysis of the Lorenz equations
Recent progress of symbolic dynamics of oneand especially two-dimensional maps has enabled us to construct symbolic dynamics for systems of ordinary differential equations (ODEs). Numerical study under the guidance of symbolic dynamics is capable to yield global results on chaotic and periodic regimes in systems of dissipative ODEs which cannot be obtained neither by purely analytical means nor...
متن کاملKneadings, Symbolic Dynamics and Painting Lorenz Chaos
A new computational technique based on the symbolic description utilizing kneading invariants is proposed, and verified for explorations of dynamical and parametric chaos in a few exemplary systems with the Lorenz attractor. The technique allows for uncovering the stunning complexity and universality of bi-parametric structures and detects their organizing centers — codimension-two T-points and...
متن کاملSymbolic dynamics and periodic orbits of the Lorenz attractor*
The butterfly-like Lorenz attractor is one of the best known images of chaos. The computations in this paper exploit symbolic dynamics and other basic notions of hyperbolicity theory to take apart the Lorenz attractor using periodic orbits. We compute all 111011 periodic orbits corresponding to symbol sequences of length 20 or less, periodic orbits whose symbol sequences have hundreds of symbol...
متن کاملThe 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...
متن کاملBifurcation analysis and dynamics of a Lorenz –type dynamical system
./files/site1/files/0Abstract1.pdfIn this paper we consider a continues Lorenz – type dynamical system. Dynamical behaviors of this system such as computing equilibrium points, different bifurcation curves and computation of normal form coefficient of each bifurcation point analytically and numerically. In particular we derived sufficient conditions for existence of Hopf and Pitchfork bifurcati...
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ژورنال
عنوان ژورنال: Chaos, Solitons & Fractals
سال: 1996
ISSN: 0960-0779
DOI: 10.1016/0960-0779(95)00046-1