添加破碎动力学中的Hopf分岔
Hopf bifurcation in addition-shattering kinetics
摘要：
在聚集-碎裂过程中，通常在较长的时间限制内达到稳定状态。这表明常微分方程组中存在不动点。下一个最简单的可能性是渐近周期运动。尽管最近在一些系统中数值检测到了振荡，但到目前为止还没有严格地建立起无休止的振荡。对于一类加法破碎过程，我们提供了令人信服的数值证据，在一定的区域$\mathcal{U}$的参数空间的永无止境的振荡。我们调查的过程承认一个不动点，成为不稳定的参数时，属于$\mathcal{U}$和永无止境的振荡有效地出现通过一个Hopf分岔。
英文摘要：
In aggregation-fragmentation processes, a steady state is usually reached in the long time limit. This indicates the existence of a fixed point in the underlying system of ordinary differential equations. The next simplest possibility is an asymptotically periodic motion. Never-ending oscillations have not been rigorously established so far, although oscillations have been recently numerically detected in a few systems. For a class of addition-shattering processes, we provide convincing numerical evidence for never-ending oscillations in a certain region $\mathcal{U}$ of the parameter space. The processes which we investigate admit a fixed point that becomes unstable when parameters belong to $\mathcal{U}$ and never-ending oscillations effectively emerge through a Hopf bifurcation.
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