The existence of positive solutions to the system of ordinary differential equations related to the Belousov-Zhabotinsky reaction is established. The key idea is to use a new successive approximation of solutions, ens...The existence of positive solutions to the system of ordinary differential equations related to the Belousov-Zhabotinsky reaction is established. The key idea is to use a new successive approximation of solutions, ensuring its positivity. To obtain the positivity and invariant region for numerical solutions, the system is discretized as difference equations of explicit form, employing operator splitting methods with linear stability conditions. Algorithm to solve the alternate solution is given.展开更多
The dynamics of a typical Belousov-Zhabotinsky(BZ)reaction with multiple time scales is investigated in this paper.Different forms of periodic bursting phenomena,and specially,three types of chaotic bursters with diff...The dynamics of a typical Belousov-Zhabotinsky(BZ)reaction with multiple time scales is investigated in this paper.Different forms of periodic bursting phenomena,and specially,three types of chaotic bursters with different structures can be obtained,which are in common with the behaviors observed in experiments.The bifurcations connecting the quiescent state and the repetitive spikes are presented to account for the occurrence of the NKoscillations as well as the different forms of chaotic bursters.The mechanism of the period-adding bifurcation sequences is explored to reveal why the length of the periods in the sequences does not change continuously with the continuous variation of the parameters.展开更多
The adaptive synchronization scheme proposed by John and Amritkar was employed into the Belousov Zhabotinsky (BZ) 4 variable Montanator model system. By the parameter adjustment, chaos synchronization has been obta...The adaptive synchronization scheme proposed by John and Amritkar was employed into the Belousov Zhabotinsky (BZ) 4 variable Montanator model system. By the parameter adjustment, chaos synchronization has been obtained. Through calculating the transient time, the optimal combination of the stiffness constant and damping constant was obtained. Furthermore, the relationships among the transient time, conditional Lyapunov exponents, the stiffness constant and damping constant were discussed. Also, the BZ system with the adaptive synchronization scheme might be used for the communication purposes.展开更多
The ferroin-catalyzed Belousov-Zhabotinsky(BZ) reaction,the oxidation of malonic acid by acidic bromate,is the most commonly investigated chemical system for understanding spatial pattern forma-tion. Various oscillato...The ferroin-catalyzed Belousov-Zhabotinsky(BZ) reaction,the oxidation of malonic acid by acidic bromate,is the most commonly investigated chemical system for understanding spatial pattern forma-tion. Various oscillatory behaviors were found from such as mixed-mode and simple period-doubling oscillations and chaos on both Pt electrode and Br-ISE at high flow rates to mixed-mode oscillations on Br-ISE only at low flow rates. The complex dynamic behaviors were qualitatively reproduced with a two-cycle coupling model proposed initially by Gy?rgyi and Field. This investigation offered a proper medium for studying pattern formation under complex temporal dynamics. In addition,it also shows that complex oscillations and chaos in the BZ reaction can be extended to other bromate-driven nonlinear reaction systems with different metal catalysts.展开更多
This paper deals with one kind of Belousov-Zhabotinskii reaction model. Linear stability is discussed for the spatially homogeneous problem firstly. Then we focus on the stationary problem with diffusion. Non-existenc...This paper deals with one kind of Belousov-Zhabotinskii reaction model. Linear stability is discussed for the spatially homogeneous problem firstly. Then we focus on the stationary problem with diffusion. Non-existence and existence of non-constant positive solutions are obtained by using implicit function theorem and Leray-Sehauder degree theory, respectively.展开更多
文摘The existence of positive solutions to the system of ordinary differential equations related to the Belousov-Zhabotinsky reaction is established. The key idea is to use a new successive approximation of solutions, ensuring its positivity. To obtain the positivity and invariant region for numerical solutions, the system is discretized as difference equations of explicit form, employing operator splitting methods with linear stability conditions. Algorithm to solve the alternate solution is given.
基金supported by the National Natural Science Foundation of China(Grant Nos.10872080 and 20976075)
文摘The dynamics of a typical Belousov-Zhabotinsky(BZ)reaction with multiple time scales is investigated in this paper.Different forms of periodic bursting phenomena,and specially,three types of chaotic bursters with different structures can be obtained,which are in common with the behaviors observed in experiments.The bifurcations connecting the quiescent state and the repetitive spikes are presented to account for the occurrence of the NKoscillations as well as the different forms of chaotic bursters.The mechanism of the period-adding bifurcation sequences is explored to reveal why the length of the periods in the sequences does not change continuously with the continuous variation of the parameters.
文摘The adaptive synchronization scheme proposed by John and Amritkar was employed into the Belousov Zhabotinsky (BZ) 4 variable Montanator model system. By the parameter adjustment, chaos synchronization has been obtained. Through calculating the transient time, the optimal combination of the stiffness constant and damping constant was obtained. Furthermore, the relationships among the transient time, conditional Lyapunov exponents, the stiffness constant and damping constant were discussed. Also, the BZ system with the adaptive synchronization scheme might be used for the communication purposes.
基金Supported by the National Natural Science Foundation of China (Grant No. 20573134) the Program for New Century Excellent Talents in Chinese Univer-sity (Grant No. NCET-05-0477)
文摘The ferroin-catalyzed Belousov-Zhabotinsky(BZ) reaction,the oxidation of malonic acid by acidic bromate,is the most commonly investigated chemical system for understanding spatial pattern forma-tion. Various oscillatory behaviors were found from such as mixed-mode and simple period-doubling oscillations and chaos on both Pt electrode and Br-ISE at high flow rates to mixed-mode oscillations on Br-ISE only at low flow rates. The complex dynamic behaviors were qualitatively reproduced with a two-cycle coupling model proposed initially by Gy?rgyi and Field. This investigation offered a proper medium for studying pattern formation under complex temporal dynamics. In addition,it also shows that complex oscillations and chaos in the BZ reaction can be extended to other bromate-driven nonlinear reaction systems with different metal catalysts.
文摘This paper deals with one kind of Belousov-Zhabotinskii reaction model. Linear stability is discussed for the spatially homogeneous problem firstly. Then we focus on the stationary problem with diffusion. Non-existence and existence of non-constant positive solutions are obtained by using implicit function theorem and Leray-Sehauder degree theory, respectively.
