Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain ...Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain some authors' results known. Secondly, by using a series of transformations, the model is reduced into a nonlinear reaction diffusion equation and then through using sine-cosine method, more exact solutions are found which contain soliton solutions.展开更多
In this work,we modify the traditi onal Brusselator model to in corporate the intermolecular interactions,based on which a systematic study is performed on the pattern formation mediated by chemical reaction and phase...In this work,we modify the traditi onal Brusselator model to in corporate the intermolecular interactions,based on which a systematic study is performed on the pattern formation mediated by chemical reaction and phase separation.It is found that if the chemical reaction dominates,the pattern formation will be inhibited by the phase separation while if the phase separation dominates,the chemical reaction will preve nt,un der certain conditi ons,the domain size from growing which results in dissipative patter ns other tha n macroscopic phase separations.展开更多
This paper is devoted to establishing a critical value of the concentration of one intermediary reactant which determines whether pattern solutions of a class of Brusselator models exist or not.We introduce a new meth...This paper is devoted to establishing a critical value of the concentration of one intermediary reactant which determines whether pattern solutions of a class of Brusselator models exist or not.We introduce a new method to compute the degree index of the related linear operator so that the obtained sufficient conditions are easier to verify than those in the known references.The proofs mainly rely on Leray-Schauder degree theory,implicit function theorem and analytical techniques.展开更多
The formation of spatial patterns is an important issue in reaction–diffusion systems.Previous studies have mainly focused on the spatial patterns in reaction–diffusion models equipped with symmetric diffusion(such ...The formation of spatial patterns is an important issue in reaction–diffusion systems.Previous studies have mainly focused on the spatial patterns in reaction–diffusion models equipped with symmetric diffusion(such as normal or fractional Laplace diffusion),namely,assuming that spatial environments of the systems are homogeneous.However,the complexity and heterogeneity of spatial environments of biochemical reactions in vivo can lead to asymmetric diffusion of reactants.Naturally,there arises an open question of how the asymmetric diffusion affects dynamical behaviors of biochemical reaction systems.To answer this,we build a general asymmetric L´evy diffusion model based on the theory of a continuous time random walk.In addition,we investigate the two-species Brusselator model with asymmetric L´evy diffusion,and obtain a general condition for the formation of Turing and wave patterns.More interestingly,we find that even though the Brusselator model with symmetric diffusion cannot produce steady spatial patterns for some parameters,the asymmetry of L´evy diffusion for this model can produce wave patterns.This is different from the previous result that wave instability requires at least a three-species model.In addition,the asymmetry of L´evy diffusion can significantly affect the amplitude and frequency of the spatial patterns.Our results enrich our knowledge of the mechanisms of pattern formation.展开更多
We discuss the dynamical behavior of a chemical network arising from the coupling of two Brusselators established by the relationship between products and substrates. Our interest is to investigate the coherence reson...We discuss the dynamical behavior of a chemical network arising from the coupling of two Brusselators established by the relationship between products and substrates. Our interest is to investigate the coherence resonance （CR） phenomena caused by noise for a coupled Brusselator model in the vicinity of the Hopf bifurcation, which can be determined by the signM-to-noise ratio （SNR）. The CR in two coupled Brusselators will be considered in the presence of the Gaussian colored noise and two uncorrelated Gaussian white noises. Simulation results show that, for the case of single noise, the SNR characterizing the degree of temporal regularity of coupled model reaches a maximum value at some optimal noise levels, and the noise intensity can enhance the CR phenomena of both subsystems with a similar trend but in different resonance degrees. Meanwhile, effects of noise intensities on CR of the second subsystem are opposite for the systems under we find that CR might be a general phenomenon in coupled two uncorrelated Gaussian white noises. Moreover, systems.展开更多
基金国家自然科学基金，NKBRD of China，Doctor Foundation of Education Commission of China
文摘Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain some authors' results known. Secondly, by using a series of transformations, the model is reduced into a nonlinear reaction diffusion equation and then through using sine-cosine method, more exact solutions are found which contain soliton solutions.
基金by the National Natural Science Foundation of China(Nos.21534002 and 21973018).
文摘In this work,we modify the traditi onal Brusselator model to in corporate the intermolecular interactions,based on which a systematic study is performed on the pattern formation mediated by chemical reaction and phase separation.It is found that if the chemical reaction dominates,the pattern formation will be inhibited by the phase separation while if the phase separation dominates,the chemical reaction will preve nt,un der certain conditi ons,the domain size from growing which results in dissipative patter ns other tha n macroscopic phase separations.
基金supported by the National Natural Science Foundation of China(No.11671359)the Science Foundation of Zhejiang Sci-Tech University under Grant No.15062173-Ysupported by the provincial Natural Science Foundation of Zhejiang(LY16A010009)
文摘This paper is devoted to establishing a critical value of the concentration of one intermediary reactant which determines whether pattern solutions of a class of Brusselator models exist or not.We introduce a new method to compute the degree index of the related linear operator so that the obtained sufficient conditions are easier to verify than those in the known references.The proofs mainly rely on Leray-Schauder degree theory,implicit function theorem and analytical techniques.
基金supported by the National Natural Science Foundation of China(Grant Nos.62066026,62363027,and 12071408)PhD program of Entrepreneurship and Innovation of Jiangsu Province,Jiangsu University’Blue Project’,the Natural Science Foundation of Jiangxi Province(Grant No.20224BAB202026)the Science and Technology Research Project of Jiangxi Provincial Department of Education(Grant No.GJJ2203316).
文摘The formation of spatial patterns is an important issue in reaction–diffusion systems.Previous studies have mainly focused on the spatial patterns in reaction–diffusion models equipped with symmetric diffusion(such as normal or fractional Laplace diffusion),namely,assuming that spatial environments of the systems are homogeneous.However,the complexity and heterogeneity of spatial environments of biochemical reactions in vivo can lead to asymmetric diffusion of reactants.Naturally,there arises an open question of how the asymmetric diffusion affects dynamical behaviors of biochemical reaction systems.To answer this,we build a general asymmetric L´evy diffusion model based on the theory of a continuous time random walk.In addition,we investigate the two-species Brusselator model with asymmetric L´evy diffusion,and obtain a general condition for the formation of Turing and wave patterns.More interestingly,we find that even though the Brusselator model with symmetric diffusion cannot produce steady spatial patterns for some parameters,the asymmetry of L´evy diffusion for this model can produce wave patterns.This is different from the previous result that wave instability requires at least a three-species model.In addition,the asymmetry of L´evy diffusion can significantly affect the amplitude and frequency of the spatial patterns.Our results enrich our knowledge of the mechanisms of pattern formation.
基金Supported by the National Natural Science Foundation of China under Grant No 61571365
文摘We discuss the dynamical behavior of a chemical network arising from the coupling of two Brusselators established by the relationship between products and substrates. Our interest is to investigate the coherence resonance （CR） phenomena caused by noise for a coupled Brusselator model in the vicinity of the Hopf bifurcation, which can be determined by the signM-to-noise ratio （SNR）. The CR in two coupled Brusselators will be considered in the presence of the Gaussian colored noise and two uncorrelated Gaussian white noises. Simulation results show that, for the case of single noise, the SNR characterizing the degree of temporal regularity of coupled model reaches a maximum value at some optimal noise levels, and the noise intensity can enhance the CR phenomena of both subsystems with a similar trend but in different resonance degrees. Meanwhile, effects of noise intensities on CR of the second subsystem are opposite for the systems under we find that CR might be a general phenomenon in coupled two uncorrelated Gaussian white noises. Moreover, systems.
