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In this paper, we report the dynamical behaviours of a
four-dimensional autonomous continuous dissipative system analysed
when the parameter is varied in the range we are interested in. The
system changes its dynamical modes between periodic motion and
quasiperiodic motion. Furthermore, the existence of two-torus is
investigated numerically by means of Lyapunov exponents. By taking
advantage of phase portraits and Poincar\'{e} sections, two types of
the two-torus are observed and proved to have the structure of ring
torus and horn torus, both of which are known to be the standard
tori. 相似文献
2.
In this paper, we report the dynamical behaviours of a four-dimenslonal autonomous continuous dissipative system analysed when the parameter is varied in the range we are interested in. The system changes its dynamical modes between periodic motion and quasiperiodic motion. Furthermore, the existence of two-torus is investigated numerically by means of Lyapunov exponents. By taking advantage of phase portraits and Poincaré sections, two types of the two-torus are observed and proved to have the structure of ring torus and horn torus, both of which are known to be the standard tori. 相似文献
3.
Laura Tedeschini-Lalli 《Journal of statistical physics》1982,27(2):365-388
A two-parameter family of nonlinear differential equations x=F(x, R, ) is studied, which allows one to connect continuously, as varies from zero to one, the different phenomenologies exhibited by a model of 5-mode truncated Navier-Stokes equations and by a 7-mode one extending it. A critical value is found for, at which the most significant phenomena of the 5-mode system either vanish or go to infinity. New phenomena arise then, leading to the 7-mode model.Supported by G.N.F.M., C.N.R. 相似文献
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