【摘 要】
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This paper studies a new class of two-dimensional rational maps exhibiting self-excited and hidden attractors.The mathematical model of these maps is firstly formulated by introducing a rational term.The analysis of existence and stabil-ity of the fixed p
【机 构】
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Faculty of Civil Engineering and Mechanics,Jiangsu University,Zhenjiang 212013,China;School of Mathe
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This paper studies a new class of two-dimensional rational maps exhibiting self-excited and hidden attractors.The mathematical model of these maps is firstly formulated by introducing a rational term.The analysis of existence and stabil-ity of the fixed points in these maps suggests that there are four types of fixed points,i.e.,no fixed point,one single fixed point,two fixed points and a line of fixed points.To investigate the complex dynamics of these rational maps with different types of fixed points,numerical analysis tools,such as time histories,phase portraits,basins of attraction,Lyapunov ex-ponent spectrum,Lyapunov(Kaplan-Yorke)dimension and bifurcation diagrams,are employed.Our extensive numerical simulations identify both self-excited and hidden attractors,which were rarely reported in the literature.Therefore,the multi-stability of these maps,especially the hidden one,is further explored in the present work.
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