This paper introduces a novel three dimensional autonomous differential system which is derived from Shimizu-Morioka *** the one hand,the rich local dynamics of it,*** distribution of equilibrium point,stability,Hopf ...
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This paper introduces a novel three dimensional autonomous differential system which is derived from Shimizu-Morioka *** the one hand,the rich local dynamics of it,*** distribution of equilibrium point,stability,Hopf bifurcation and so on,are *** the other hand,the nonexistence of homoclinic and existence of heteroclinic orbits of it is also rigorously studied under some certain parameters by the classic method--employing Lyapunov functional together with theωlimit set andαlimit *** particular,the local stability of the symmetrical equilibria yields the global stability of them.
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