Li Hsing-Ya, Chien Yu-Shu, Chiou Ming-Shen
Department of Chemical Engineering, National United University, Miaoli 36063, Taiwan.
Department of Chemical and Materials Engineering, National Chin-Yi University of Technology, Taichung, Taiwan.
Chaos. 2024 Nov 1;34(11). doi: 10.1063/5.0231992.
The nonlinear dynamical behavior in a complex isothermal reaction network involving heterogeneous catalysis is studied. The method first determines the multiple steady states in the reaction network. This is followed by an analysis of bifurcation continuations to identify several kinds of bifurcations, including limit point, Bogdanov-Takens, generalized Hopf, period doubling, and generalized period doubling. Numerical simulations are performed around the period doubling and generalized period doubling bifurcations. Rich nonlinear behaviors are observed, including simple sustained oscillations, mixed-mode oscillations, non-mixed-mode chaotic oscillations, and mixed-mode chaotic oscillations. Concentration-time plots, 2D phase portraits, Poincaré maps, maximum Lyapunov exponents, frequency spectra, and cascade of bifurcations are reported. Period-doubling and period-adding routes leading to chaos are observed. Maximum Lyapunov exponents are positive for all the chaotic cases, but they are also positive for some non-chaotic orbits. This result diminishes the reliability of using maximum Lyapunov exponents as a tool for determining chaos in the network under study.
研究了包含多相催化的复杂等温反应网络中的非线性动力学行为。该方法首先确定反应网络中的多个稳态。随后进行分岔延续分析，以识别几种分岔类型，包括极限点、博格达诺夫 - 塔肯斯、广义霍普夫、倍周期和广义倍周期分岔。围绕倍周期和广义倍周期分岔进行了数值模拟。观察到丰富的非线性行为，包括简单持续振荡、混合模式振荡、非混合模式混沌振荡和混合模式混沌振荡。报告了浓度 - 时间图、二维相图、庞加莱映射、最大李雅普诺夫指数、频谱和分岔级联。观察到通向混沌的倍周期和加周期路径。所有混沌情况的最大李雅普诺夫指数均为正，但一些非混沌轨道的最大李雅普诺夫指数也为正。这一结果降低了使用最大李雅普诺夫指数作为确定所研究网络中混沌的工具的可靠性。
