Lemarchand A, Gorecki J, Gorecki A, Nowakowski B
Sorbonne Universités, UPMC Univ Paris 06, Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), 4 place Jussieu, case courrier 121, 75252 Paris Cedex 05, France and CNRS, LPTMC, UMR 7600, Paris, France.
Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland and Faculty of Mathematics and Life Science, UKSW, Warsaw, Poland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Feb;89(2):022916. doi: 10.1103/PhysRevE.89.022916. Epub 2014 Feb 18.
We perform the stochastic analysis of a thermochemical system using a master equation which describes a chemical reaction and includes discrete and continuous temperature jumps. We study the time evolution of the system selecting the temperature of the thermostat as an easily tunable control parameter. Depending on the thermostat temperature, the system can be in an excitable, oscillatory, or stationary regime. Stochastic time series for the system temperature are generated and the distributions of interspike intervals are analyzed in the three dynamical regimes separated by a homoclinic bifurcation and a Hopf bifurcation. Different constructive roles of internal fluctuations are exhibited. A noise-induced transition is observed in the vicinity of the Hopf bifurcation. Coherence resonance and stochastic resonance are found in the oscillatory regime. In a range of thermostat temperatures, a nontrivial behavior of the highly nonlinear system is revealed by the existence of both a minimum and a maximum in the scaled standard deviation of interspike intervals as a function of particle number. This high sensitivity to system size illustrates that controlling dynamics in nanoreactors may remain a difficult task.
我们使用主方程对热化学系统进行随机分析，该主方程描述了一个化学反应，并包括离散和连续的温度跳跃。我们通过选择恒温器的温度作为易于调节的控制参数来研究系统的时间演化。根据恒温器温度的不同，系统可以处于可激发、振荡或稳态 regime。生成了系统温度的随机时间序列，并分析了由同宿分岔和霍普夫分岔分隔的三种动力学 regime 中的尖峰间隔分布。展示了内部涨落的不同建设性作用。在霍普夫分岔附近观察到噪声诱导的转变。在振荡 regime 中发现了相干共振和随机共振。在一定范围的恒温器温度下，作为粒子数函数的尖峰间隔的标度标准差中存在最小值和最大值，揭示了高度非线性系统的非平凡行为。这种对系统尺寸的高敏感性表明，控制纳米反应器中的动力学可能仍然是一项艰巨的任务。
