一类保守系统向类耗散系统的过渡

TRANSITION FROM A CONSERVATIVE SYSTEM TO A QUASI-DISSIPATIVE ONE

在已经报道的加保护的张弛振荡电路模型中 ,随着保护区从无到有 ,从小到大 ,系统连续地逐渐从一个典型的保守系统转变为一个“类耗散系统”.在选择的一组参数下 ,当保护区大小等于 0时 ,相平面呈现典型的保守系统中的混沌海 .随着保护区逐渐增大 ,系统函数的不连续边界出现 ,而且系统在此边界处的能量跳跃也逐渐增大 .使得系统的“类保守性”逐渐减弱 ,而“类耗散性”逐渐加强 .在此过程中 ,原来的混沌海中的迭代轨道逐渐演变为一个由不连续边界象集的归宿构成的随机网 .最后 ,当类耗散性很强时 ,这个随机网又演变为非常类似于耗散系统中的混沌吸引子 .计算了这时的“混沌类吸引子”

In the electronic relaxation oscillating circuit with over-voltage protection was reported in this same journal.As the protected region increases from zero the system gradually transfers from a typical conservative one to a 'quasi-dissipative'one.In the chosen group of parameters,when the protected region is zero the phase plane displays a chaotic sea that exists in typical conservative systems.As it gradually increases,the discontinuous border of the system function appears,and the jump of the system energy at it also becomes bigger.That makes the 'quasi-conservative'property of the system weaker,and the 'quasi-dissipative'property stronger.In this process the iteration trajectory in the aforementioned chaotic sea gradually changes to a stochastic web constructed by the end results of the image set of the discontinuous border.At last,when the quasi-dissipative property becomes very strong,this stochastic web becomes very similar to a chaotic attractor in a dissipative system.The paper numerically computed the fractal dimension of the chaotic 'quasi-attractor'in the case.