Dynamic elements of mixed‐mode oscillations and chaos in a peroxidase–oxidase model network
Dynamic elements of mixed‐mode oscillations and chaos in a peroxidase–oxidase model network
复制标题
过氧化物酶-氧化酶模型网络中混合模式振荡和混沌的动态元素
DOI：
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发表时间：
1989
期刊：
影响因子：
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通讯作者：
B. L. Clarke
中科院分区：
文献类型：
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作者：
B. Aguda;R. Larter;B. L. Clarke
对于过氧化物酶-氧化酶反应的四物种Olsen模型，确定了三个动力学元件：DE-1、DE-2和DE-3。De-1是有阻尼洛特卡振荡器，它往往会产生较小的振幅振荡。De-2是一个开关，负责小幅度和大幅度振荡之间的转换。当中间产物浓度较低时，De-3是可逆的O2通量，它主导着整个网络的动力学。在现实机理中，DE-1与过氧化物酶催化循环相一致，而DE-2与涉及化合物III的反应相一致。给出了不同参数对这三个动力学要素影响的混沌路径的数值模拟。给出了伴随着混沌振荡的奇怪吸引子的演化图像。如吸引子和Poincare Next-Return地图的Poincare部分所示，此吸引子的层随着偶周期和奇周期固定点经历倍增周期的级联而发展。
Three dynamic elements, DE‐1, DE‐2, and DE‐3, are identified for the four‐species Olsen model of the peroxidase–oxidase reaction. DE‐1 is the damped Lotka oscillator which tends to generate smaller amplitude oscillations. DE‐2 is a switch responsible for the transitions between a small and a larger amplitude oscillation. DE‐3 is the reversible flux of O2 which dominates the dynamics of the full network while the concentrations of the intermediates are low. DE‐1 is identified with the peroxidase catalytic cycle and DE‐2 with a reaction involving compound III in the realistic mechanism. Numerical simulations on the route to chaos are presented for varying parameters affecting the three dynamic elements. Pictures of the evolution of the strange attractor that accompanies chaotic oscillations are given. As shown in the Poincare sections of the attractor and Poincare next‐return maps, the layers of this attractor develop as even‐ and odd‐period fixed points undergo cascades of period doubling.