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Bifurcations and chaos in fractional-order simplified Lorenz system. (English) Zbl 1193.34005

Summary: The dynamics of fractional-order systems have attracted increasing attention in recent years. In this paper, we numerically study the bifurcations and chaotic behaviors in the fractional-order simplified Lorenz system using the time-domain scheme. Chaos does exist in this system for a wide range of fractional orders, both less than and greater than three. Complex dynamics with interesting characteristics are presented by means of phase portraits, bifurcation diagrams and the largest Lyapunov exponent. Both the system parameter and the fractional order can be taken as bifurcation parameters, and the range of existing chaos is different for different parameters. The lowest order we found for this system to yield chaos is 2.62.

MSC:

34A08 Fractional ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
34D08 Characteristic and Lyapunov exponents of ordinary differential equations

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