Dynamics of a class of fractional-order nonautonomous Lorenz-type systems
1Department of Mathematics, Shandong University, Weihai 264209, Shandong, China.
Abstract:
The dynamical properties of a class of fractional-order Lorenz-type systems with quasi-periodic time-varying parameters are studied, where the fractional derivative is defined in the sense of Caputo. The effective non-integer dimension β is the sum of all the fractional orders. Deferring from the fractional-order autonomous Lorenz systems, the present nonautonomous systems have two critical values, β* and β*, of the effective non-integer dimension, 0<β*<β*<3, under which there exist a transition from chaos to quasi-periodic dynamics for some β near β* and a transition from quasi-periodic motion to regular dynamics (diverging to infinity) for some β near β*. The 0-1 test is applied to verify the existence of such strange dynamics.
Related Concept Videos
01:21First Order Systems
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
01:18Second Order systems II
01:26Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
01:21Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
01:23Linear time-invariant Systems
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
01:20Second Order systems I
By reinterpreting the system, one can derive the closed-loop transfer function, which...