1-D映象收敛于渐近状态的标度性研究
Convergence towards asymptotic state in 1-D mappings: a scaling investigation
摘要：
通过考虑由数值模拟支持并由理论描述证实的唯象描述来表征一维类逻辑映射中衰减到渐进稳态的特征。当控制参数变化时，系统在不动点处出现分岔。我们验证了在两个分叉点;跨临界，干草叉和倍周期分叉，该稳定点的衰减的特征在于通过一个齐次函数与三个临界指数取决于映射的非线性。在分叉点附近，不动点的衰减是指数的，松弛时间由幂律给出，其斜率与非线性无关。该形式具有一般性，并可推广到其他耗散映射。
英文摘要：
Decay to asymptotic steady state in one-dimensional logistic-like mappings is characterized by considering a phenomenological description supported by numerical simulations and confirmed by a theoretical description. As the control parameter is varied bifurcations in the fixed points appear. We verified at the bifurcation point in both; the transcritical, pitchfork and period-doubling bifurcations, that the decay for the stationary point is characterized via a homogeneous function with three critical exponents depending on the nonlinearity of the mapping. Near the bifurcation the decay to the fixed point is exponential with a relaxation time given by a power law whose slope is independent of the nonlinearity. The formalism is general and can be extended to other dissipative mappings.
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