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In this article, we study the planar piecewise differential systems formed by two linear differential systems separated by a straight line, such that both linear differential have no equilibria, neither real nor virtual. When the piecewise differential system is continuous, we show that the system has no limit cycles. But when the piecewise differential system is discontinuous, we show that it can...
Our work focuses on the study of a kind of new bifurcation behavior about limit cycles (namely double bifurcation) for a class of cubic Kolmogorov model with a degenerate critical point (1, 1). The positive critical point (1, 1) is a 3-multiple nilpotent fine focus which can become a fine focus of 5th order. By analyzing the change in stability, we show (1, 1) can yield 4 limit cycles. Moreover, the...
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