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Chaos in the fractional-order Lorenz system. (English) Zbl 1169.65115

Summary: We investigate the chaotic behaviours in the fractional-order Lorenz system. By utilizing the fractional calculus techniques, we find that chaos exists in the fractional-order Lorenz system of order less than 3. The lowest order we found to have chaos in this system is 2.97.

MSC:

65P20 Numerical chaos
34L30 Nonlinear ordinary differential operators
49M05 Numerical methods based on necessary conditions
65E05 General theory of numerical methods in complex analysis (potential theory, etc.)
68W25 Approximation algorithms
90C59 Approximation methods and heuristics in mathematical programming
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