Several Chaotic Analysis of Lorenz System (original) (raw)
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Turkish Journal of Electrical Engineering and Computer Sciences, 2010
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The classical Lorenz system is considered. For many years, this system has been the subject of study by numerous authors. However, until now the structure of the Lorenz attractor is not clear completely yet, and the most important question at present is to understand the bifurcation scenario of chaos transition in this system. Using some numerical results and our bifurcational geometric approach, we present a new scenario of chaos transition in the classical Lorenz system.
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The apparent failure of the linear stability analysis to predict accurately the transition point from steady to chaotic solutions in Lorenz equations motivates this study. A weak nonlinear solution to the problem is shown to produce an accurate analytical expression for the transition point as long as the condition of validity and consequent accuracy of the latter solution is fulfilled. The analytical results are compared to accurate computational solutions, showing an excellent fit within the validity domain of the analytical solution.
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Chaos Solitons & Fractals, 2004
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