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A novel decentralized non-integer order controller applied on nonlinear fractional-order composite system(NFOCS) is proposed. In addition, some novel results for the asymptotic stabilization are shown with fractional parameter α∈0,1. First, we derive certain novel results useful for the Mittag-Leffler function. Then, we design a new decentralized fractional-order controller for the NFOCS according to the novel results applied to Mittag-Leffler function. Next, this novel asymptotic stabilization condition has been proposed. Compared with other controllers our controller has wider control gain range and weaker requirements. Moreover, we solve the asymptotic stabilization problem of the NFOCS with time delays via the novel controller. In the end, four general examples are performed to show the progressiveness of the new fractional-order decentralized controller.
RESUMO
Behavioral choice is ubiquitous across a wide range of interactive decision-making processes and a myriad of scientific disciplines. With regard to this issue, one entitative problem is actually to understand how collective social behaviors form and evolve among populations when they face a variety of conflict alternatives. In this paper, a selection-drift dynamic model is formulated to characterize the behavior imitation and exploration processes in social populations. Based on the proposed framework, several typical behavior evolution patterns, including behavioral flocking, collapse, and oscillation, are reproduced with different kinds of behavior networks. Interestingly, for the selection-drift dynamics on homogeneous symmetric behavior networks, we unveil the phase transition from behavioral flocking to collapse and derive the bifurcation diagram of the evolutionary stable behaviors in social behavior evolution. While via analyzing the survival conditions of the best behavior on heterogeneous symmetric behavior networks, we propose a selection-drift mechanism to guarantee consensus at the optimal behavior. Moreover, when the selection-drift dynamics on asymmetric behavior networks is simulated, it is shown that breaking the symmetry in behavior networks can induce various behavioral oscillations. These obtained results may shed new insights into understanding, detecting, and further controlling how social norm and cultural trends evolve.
RESUMO
AIM: To detect free and hydrolysable gallic acid in Acer Truncatum Bunge by HPLC. METHODS: A method for determining gallic acid in leaves of Acer Truncatum Bunge.The operating conditions HPLC were Diamonsil C_18 column(5 ?m,4.6 mm?250 mm) at room temperature,methanol-0.025 mol/L phosphoric acid solution(15∶85) as mobile phase at a flow of 1.0 mL/min and UV detection at 272 nm. RESULTS: The contents of free and hydrolysable gallic acid were 0.045% and 1.546%,repectively.The relative standard deviations of free and hydrolysable gallic acid were 1.06% and 2.43%,respectively. CONCLUSION: The contents of free and hydrolysable gallic acid in Acer Truncatum Bunge in different periods are different.