In this paper, a non-existence condition for homoclinic and heteroclinic orbits in n-dimensional, continuous-time, and smooth systems is obtained, Based on this result and an elementary example, it can be conjectured ...In this paper, a non-existence condition for homoclinic and heteroclinic orbits in n-dimensional, continuous-time, and smooth systems is obtained, Based on this result and an elementary example, it can be conjectured that there is a fourth kind of chaos in polynomial ordinary differential equation （ODE） systems characterized by the nonexistence of homoclinic and heteroclinic orbits.展开更多
The Lorenz mapping is a discretization of a pair of differential equations.It illustrates the pertinence of computational chaos.We describe complex dynamics,bifurcations,and chaos in the map.Fractal basins are display...The Lorenz mapping is a discretization of a pair of differential equations.It illustrates the pertinence of computational chaos.We describe complex dynamics,bifurcations,and chaos in the map.Fractal basins are displayed by numerical simulation.展开更多
文摘In this paper, a non-existence condition for homoclinic and heteroclinic orbits in n-dimensional, continuous-time, and smooth systems is obtained, Based on this result and an elementary example, it can be conjectured that there is a fourth kind of chaos in polynomial ordinary differential equation （ODE） systems characterized by the nonexistence of homoclinic and heteroclinic orbits.
文摘The Lorenz mapping is a discretization of a pair of differential equations.It illustrates the pertinence of computational chaos.We describe complex dynamics,bifurcations,and chaos in the map.Fractal basins are displayed by numerical simulation.
