Straube Ronny, Flockerzi Dietrich, Müller Stefan C, Hauser Marcus J B
Abteilung Biophysik, Institut für Experimentelle Physik, Otto-von-Guericke Universität, Universitätsplatz 2, D-39106 Magdeburg, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Dec;72(6 Pt 2):066205. doi: 10.1103/PhysRevE.72.066205. Epub 2005 Dec 6.
The transition from simple periodic to bursting behavior in a three-dimensional model system of the hemin-hydrogen-peroxide-sulfite pH oscillator is investigated. A two-parameter continuation in the flow rate and the hemin decay rate is performed to identify the region of complex dynamics. The bursting oscillations emerge subsequent to a cascade of period-doubling bifurcations and the formation of a chaotic attractor in parameter space where they are found to be organized in periodic-chaotic progressions. This suggests that the bursting oscillations are not associated with phase-locked states on a two-torus. The bursting behavior is classified by a bifurcation analysis using the intrinsic slow-fast structure of the dynamics. In particular, we find a slowly varying quasispecies (i.e., a linear combination of two species) which acts as an "internal" or quasistatic bifurcation parameter for the remaining two-dimensional subsystem. A systematic two-parameter continuation in the internal parameter and one of the external bifurcation parameters reveals a transition in the bursting mechanism from sub-Hopf/fold-cycle to fold/sub-Hopf type. In addition, the slow-fast analysis provides an explanation for the origin of quasiperiodic behavior in the hemin system, even though the underlying mechanism might be of more general importance.
研究了血红素-过氧化氢-亚硫酸盐pH振荡器三维模型系统中从简单周期行为到爆发行为的转变。在流速和血红素衰减率方面进行了双参数延拓，以确定复杂动力学区域。爆发振荡在一系列倍周期分岔以及参数空间中混沌吸引子形成之后出现，在该参数空间中它们被发现以周期-混沌序列组织起来。这表明爆发振荡与二维环面上的锁相状态无关。利用动力学的内在快慢结构，通过分岔分析对爆发行为进行分类。特别地，我们发现一个缓慢变化的拟物种（即两个物种的线性组合），它作为其余二维子系统的“内部”或准静态分岔参数。在内部参数和一个外部分岔参数方面进行系统的双参数延拓，揭示了爆发机制从亚霍普夫/折叠周期到折叠/亚霍普夫类型的转变。此外，快慢分析为血红素系统中准周期行为的起源提供了解释，尽管其潜在机制可能具有更普遍的重要性。
