AUTO-DARBOUX TRANSFORMATION AND EXACT SOLUTIONS OF THE BRUSSELATOR REACTION DIFFUSION MODEL

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.

A different approach for conformable fractional biochemical reaction–diffusion models

This paper attempts to shed light on three biochemical reaction-diffusion models:conformable fractional Brusselator,conformable fractional Schnakenberg,and conformable fractional Gray-Scott.This is done using conformable residual power series(hence-form,CRPS)technique which has indeed,proved to be a useful tool for generating the solution.Interestingly,CRPS is an effective method of solving nonlinear fractional differential equations with greater accuracy and ease.

Resonance Analyses for a Noisy Coupled Brusselator Model

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.

共生理论视角下区域创新生态系统演化特征研究

基于科学转移思路,将耗散结构理论中的Brusselator经典模型移植到区域创新生态系统演化分析中,同时,结合共生理论,围绕共生单元、结构与模式、网络与环境等生态特征,构建“创新投入—创新环境”要素指标体系,进而运用“全局熵—突变级数”评价模型刻画系统耗散演化过程。基于对2013-2020年我国四大国家级城市群及毗邻省份的区域创新生态系统耗散演化状态进行实证分析,研究发现:(1)我国四大城市群及毗邻省份的区域创新生态系统是一个开放性系统,同时满足小幅涨落、非线性耦合等耗散结构形成条件;(2)样本点耗散评价值呈正向演化,说明系统逐步向耗散结构演化,2015—2020年四大城市群及毗邻省份的创新环境(经济、市场、技术)显著优化,对区域创新活力及创新成果转化有积极的促进作用;(3)样本点区域创新生态系统的耗散演化持续向高区域创新投入—高水平区域创新环境方向发展。基于实证分析结果,从打造区域创新中心、完善协同体制机制、培育企业主体以及形成良性循环等方面对我国区域创新生态系统发展提出对策建议。

高技术产业创新生态系统耗散演化研究--运用Brusselator模型对中国省级区域的经验分析

高技术产业创新生态系统的耗散演化可以促进创新驱动的高质量发展,并缓解区域创新发展不平衡的问题。对Brusselator模型进行经济学转译,构建“创新投入—创新环境”二维框架的评价指标体系,可以推导高技术产业创新生态系统形成耗散结构的判定条件,并可进一步运用“全局熵—突变级数”评价模型刻画系统耗散演化的过程。采用2013—2019年中国30个省级区域高技术产业相应数据的分析表明:北京、天津、上海的高技术产业创新生态系统已形成耗散结构,大部分地区虽未形成耗散结构但正向耗散结构演进;样本地区高技术产业创新生态系统的“创新投入—创新环境”二维框架整体呈现“Ⅲ象限→Ⅱ象限→Ⅰ象限”的演化趋势,且“创新投入—创新环境”的评价值趋于提高,同时各地也具有不同的耗散演化特征。在增加高技术产业创新投入的同时,更要致力于创新环境的改善,并积极构建创新主体的协同创新网络;各地区既要采取差异化发展策略,也应促进区域间的协调发展,以进一步推动高技术产业创新生态系统的耗散演进。

Numerical simulation and analysis of complex patterns in a two-layer coupled reaction diffusion system

The resonance interaction between two modes is investigated using a two-layer coupled Brusselator model. When two different wavelength modes satisfy resonance conditions, new modes will appear, and a variety of superlattice patterns can be obtained in a short wavelength mode subsystem. We find that even though the wavenumbers of two Turing modes are fixed, the parameter changes have influences on wave intensity and pattern selection. When a hexagon pattern occurs in the short wavelength mode layer and a stripe pattern appears in the long wavelength mode layer, the Hopf instability may happen in a nonlinearly coupled model, and twinkling-eye hexagon and travelling hexagon patterns will be obtained. The symmetries of patterns resulting from the coupled modes may be different from those of their parents, such as the cluster hexagon pattern and square pattern. With the increase of perturbation and coupling intensity, the nonlinear system will con- vert between a static pattern and a dynamic pattern when the Turing instability and Hopf instability happen in the nonlinear system. Besides the wavenumber ratio and intensity ratio of the two different wavelength Turing modes, perturbation and coupling intensity play an important role in the pattern formation and selection. According to the simulation results, we find that two modes with different symmetries can also be in the spatial resonance under certain conditions, and complex patterns appear in the two-layer coupled reaction diffusion systems.

Kinetic Pattern Formation with Intermolecular Interactions:A Modified Brusselator Model

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.

Homotopy perturbation aided optimization procedure with applications to oscillatory fractional order nonlinear dynamical systems

This paper presents an approximate solution of nonlinear fractional differential equations(FDEs)that exhibit an oscillatory behavior by using a metaheuristic technique.The solutions of the governing equations are approximated by using homotopy perturbation method(HPM)along with the fractional derivative in the Caputo sense.The designed methodology is based on a weighted series of HPM in conjunction with a nature-inspired algorithm.The idea is instantly fascinated by the researchers on the consequent implementation of nature-inspired learning algorithms such as a Cuckoo search algorithm(CSA).The usage of CSA has accelerated the minimized search path of error to the convergent values of the solution.The validity and accuracy of the proposed technique are ascertained by calculating the approximate solution and the error norms which ensure the convergence of the approximation that can be further increased.The critical analysis is also provided by the numerical simulation of two different test models.Discussion of key points has been determined by the tabulation of numerical values and graphs.Comparative study of the results with known numerical technique is also performed.

Moving Finite Element Simulations for Reaction-Diffusion Systems

This work is concerned with the numerical simulations for two reactiondiffusion systems,i.e.,the Brusselator model and the Gray-Scott model.The numerical algorithm is based upon a moving finite element method which helps to resolve large solution gradients.High quality meshes are obtained for both the spot replication and the moving wave along boundaries by using proper monitor functions.Unlike[33],this work finds out the importance of the boundary grid redistribution which is particularly important for a class of problems for the Brusselator model.Several ways for verifying the quality of the numerical solutions are also proposed,which may be of important use for comparisons.