Pub Date : 2023-10-01DOI: 10.46793/match.91-2.453m
Eduardo R. Mendoza, Dylan Antonio SJ. Talabis, Editha C. Jose, Lauro L. Fontanil
A kinetic system has an absolute concentration robustness (ACR) for a molecular species if its concentration remains the same in every positive steady state of the system. Just recently, a condition that sufficiently guarantees the existence of an ACR in a rank-one mass-action kinetic system was found. In this paper, it will be shown that this ACR criterion does not extend in general to power-law kinetic systems. Moreover, we also discussed in this paper a necessary condition for ACR in multistationary rank-one kinetic system which can be used in ACR analysis. Finally, a concept of equilibria variation for kinetic systems which are based on the number of the system's ACR species will be introduced here.
{"title":"Absolute Concentration Robustness in Rank-One Kinetic Systems","authors":"Eduardo R. Mendoza, Dylan Antonio SJ. Talabis, Editha C. Jose, Lauro L. Fontanil","doi":"10.46793/match.91-2.453m","DOIUrl":"https://doi.org/10.46793/match.91-2.453m","url":null,"abstract":"A kinetic system has an absolute concentration robustness (ACR) for a molecular species if its concentration remains the same in every positive steady state of the system. Just recently, a condition that sufficiently guarantees the existence of an ACR in a rank-one mass-action kinetic system was found. In this paper, it will be shown that this ACR criterion does not extend in general to power-law kinetic systems. Moreover, we also discussed in this paper a necessary condition for ACR in multistationary rank-one kinetic system which can be used in ACR analysis. Finally, a concept of equilibria variation for kinetic systems which are based on the number of the system's ACR species will be introduced here.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136159900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.46793/match.90-3.685m
P. Mafuta
{"title":"Degree Distance in Graphs with Forbidden Subgraphs","authors":"P. Mafuta","doi":"10.46793/match.90-3.685m","DOIUrl":"https://doi.org/10.46793/match.90-3.685m","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73569827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.46793/match.90-3.729l
Qiuping Li, Liangwen Tang
The graph G of order n is an L-borderenergetic graph which means it has the same Laplacian energy as the complete graph Kn. In this paper, we find that the combination of complete bipartite graphs and stars can construct infinite numbers of infinite classes L-borderenergetic graphs. We give two infinite numbers of infinite classes L-borderenergetic graphs and two infinite classes Lborderenergetic graphs under the operators union, join and their mixed. This research could provide experience for further study the structural characteristics of L-borderenergetic graphs.
{"title":"Infinite Numbers of Infinite Classes L-Borderenergetic Graphs","authors":"Qiuping Li, Liangwen Tang","doi":"10.46793/match.90-3.729l","DOIUrl":"https://doi.org/10.46793/match.90-3.729l","url":null,"abstract":"The graph G of order n is an L-borderenergetic graph which means it has the same Laplacian energy as the complete graph Kn. In this paper, we find that the combination of complete bipartite graphs and stars can construct infinite numbers of infinite classes L-borderenergetic graphs. We give two infinite numbers of infinite classes L-borderenergetic graphs and two infinite classes Lborderenergetic graphs under the operators union, join and their mixed. This research could provide experience for further study the structural characteristics of L-borderenergetic graphs.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86035903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.46793/match.90-3.709t
Liangwen Tang, Mugang Lin, Qiuping Li
{"title":"Graph Energy Change on Edge Deletion","authors":"Liangwen Tang, Mugang Lin, Qiuping Li","doi":"10.46793/match.90-3.709t","DOIUrl":"https://doi.org/10.46793/match.90-3.709t","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88517532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.46793/match.90-3.743t
Hafsa Tabassum, P. Kaemawichanurat, A. Adeela, Nathakhun Wiroonsri
The sum of the absolute values of the eigenvalues of the graph’s adjacency matrix is known as its ordinary energy. Based on the eigenvalues of a range of other graph matrices, several other equivalent energies are being considered. In this work, we considered ordinary energy, Laplacian, Randi´c, incidence, and Sombor energy to analyze their relationship using polynomial regression. The performance of each model is exceptional with cross-validation RMSE mostly below 1.
{"title":"Relationship between Ordinary, Laplacian, Randić, Incidence, and Sombor Energies of Trees","authors":"Hafsa Tabassum, P. Kaemawichanurat, A. Adeela, Nathakhun Wiroonsri","doi":"10.46793/match.90-3.743t","DOIUrl":"https://doi.org/10.46793/match.90-3.743t","url":null,"abstract":"The sum of the absolute values of the eigenvalues of the graph’s adjacency matrix is known as its ordinary energy. Based on the eigenvalues of a range of other graph matrices, several other equivalent energies are being considered. In this work, we considered ordinary energy, Laplacian, Randi´c, incidence, and Sombor energy to analyze their relationship using polynomial regression. The performance of each model is exceptional with cross-validation RMSE mostly below 1.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82363447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.46793/match.90-3.673m
S. Majstorović
{"title":"Maximizing Graovac-Ghorbani Index of Trees with Fixed Maximum Degree","authors":"S. Majstorović","doi":"10.46793/match.90-3.673m","DOIUrl":"https://doi.org/10.46793/match.90-3.673m","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82637582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.46793/match.90-3.773a
Deekshitha Vivek Anchan, S. D’souza, H. J. Gowtham, P. G. Bhat
{"title":"Sombor Energy of a Graph with Self-Loops","authors":"Deekshitha Vivek Anchan, S. D’souza, H. J. Gowtham, P. G. Bhat","doi":"10.46793/match.90-3.773a","DOIUrl":"https://doi.org/10.46793/match.90-3.773a","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91052705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.46793/match.90-3.581c
Mengxin Chen
This paper reports the Hopf bifurcation and self-organization pattern of a modified Brusselator model. The model is a non-standard Brusselator model, it involves the nonlinear restraint term. For the non-diffusive model, we give the types of unique positive equilibrium. It is found that the unique positive equilibrium may be focus, node, or center and we establish their stability, respectively. Especially, there exists the spatial homogeneous Hopf bifurcation when the equilibrium is a center. The first Lyapunov number technique is applied to perform the direction of the spatial homogeneous Hopf bifurcation. In the sequel, the occurrence conditions of the Turing instability and the spatial inhomogeneous Hopf bifurcation are given for the diffusive model. Moreover, by using the normal form theory, we show that the Hopf bifurcation is supercritical or subcritical. Finally, the self-organization patterns induced by the Turing instability and periodic solutions resulting from the Hopf bifurcation are displayed by employing numerical simulations. Our theoretical predictions and numerical results reveal that the modified Brusselator model enjoys the temporal period oscillation and spatial oscillation due to the Hopf bifurcation and Turing instability, respectively. These results may help us to figure out the spatio-temporal dynamics of such modified Brusselator model.
{"title":"Hopf Bifurcation and Self-Organization Pattern of a Modified Brusselator Model","authors":"Mengxin Chen","doi":"10.46793/match.90-3.581c","DOIUrl":"https://doi.org/10.46793/match.90-3.581c","url":null,"abstract":"This paper reports the Hopf bifurcation and self-organization pattern of a modified Brusselator model. The model is a non-standard Brusselator model, it involves the nonlinear restraint term. For the non-diffusive model, we give the types of unique positive equilibrium. It is found that the unique positive equilibrium may be focus, node, or center and we establish their stability, respectively. Especially, there exists the spatial homogeneous Hopf bifurcation when the equilibrium is a center. The first Lyapunov number technique is applied to perform the direction of the spatial homogeneous Hopf bifurcation. In the sequel, the occurrence conditions of the Turing instability and the spatial inhomogeneous Hopf bifurcation are given for the diffusive model. Moreover, by using the normal form theory, we show that the Hopf bifurcation is supercritical or subcritical. Finally, the self-organization patterns induced by the Turing instability and periodic solutions resulting from the Hopf bifurcation are displayed by employing numerical simulations. Our theoretical predictions and numerical results reveal that the modified Brusselator model enjoys the temporal period oscillation and spatial oscillation due to the Hopf bifurcation and Turing instability, respectively. These results may help us to figure out the spatio-temporal dynamics of such modified Brusselator model.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77839662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.46793/match.90-3.563f
B. Ferčec, M. Mencinger, T. Petek, O. O. Aybar, I. K. Aybar
Glycolysis, one of the leading metabolic pathways, involves many different periodic oscillations emerging at positive steady states of the biochemical models describing this essential process. One of the models employing the molecular diffusion of intermediates is the Higgins biochemical model to explain sustained oscillations. In this paper, we investigate the center-focus problem for the minimal Higgins model for general values of the model parameters with the help of computational algebra. We demonstrate that the model always has a stable focus point by finding a general form of the first Lyapunov number. Then, varying two of the model parameters, we obtain the first three coefficients of the period function for the stable focus point of the model and prove that the singular point is actually a bi-weak monodromic equilibrium point of type [1, 2]. Additionally, we prove that there are two (small) intervals for a chosen parameter a > 0 for which one critical period bifurcates from this singular point after small perturbations
{"title":"Qualitative Analysis of the Minimal Higgins Model of Glycolysis","authors":"B. Ferčec, M. Mencinger, T. Petek, O. O. Aybar, I. K. Aybar","doi":"10.46793/match.90-3.563f","DOIUrl":"https://doi.org/10.46793/match.90-3.563f","url":null,"abstract":"Glycolysis, one of the leading metabolic pathways, involves many different periodic oscillations emerging at positive steady states of the biochemical models describing this essential process. One of the models employing the molecular diffusion of intermediates is the Higgins biochemical model to explain sustained oscillations. In this paper, we investigate the center-focus problem for the minimal Higgins model for general values of the model parameters with the help of computational algebra. We demonstrate that the model always has a stable focus point by finding a general form of the first Lyapunov number. Then, varying two of the model parameters, we obtain the first three coefficients of the period function for the stable focus point of the model and prove that the singular point is actually a bi-weak monodromic equilibrium point of type [1, 2]. Additionally, we prove that there are two (small) intervals for a chosen parameter a > 0 for which one critical period bifurcates from this singular point after small perturbations","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81526778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.46793/match.90-3.609x
Changjin Xu, Qing Cui, Zixin Liu, Yuanlu Pan, Xiaohan Cui, Wei-Bo Ou, Mati ur Rahman, Muhammad Farman, Shabir Ahmad, A. Zeb
Fractional-order differential models plays a pivotal role in depicting the relationship among concentration changes of various chemical substances in chemistry. In this current study, we will explore the dynamics of a delayed chemostat model. First of all, we prove that the solution of the delayed chemostat model exists and is unique by virtue of fixed point theorem. Secondly, we demonstrate that the solution of the delayed chemostat model is non-negative by applying some suitable inequality strategies. Thirdly, the boundedness of the solution to the delayed chemostat model is explored via constructing a reasonable function. Fourthly, the Hopf bifurcation and stability of the delayed chemostat model are dealt with by exploiting the stability criterion and bifurcation theory on fractional dynamical system. Fifthly, the stability domain and Hopf bifurcation of the delayed chemostat model are resoundingly controlled by making use of an extended hybrid controller. Sixthly, the stability domain and Hopf bifurcation of the delayed chemostat model are effectively adjusted by making use of an another extended hybrid controller. The role of delay in this chemostat model is revealed. Seventhly, software experiments are given to illustrate the rightness of the gained key conclusions. The acquired outcomes of this work are perfectly innovative and have crucial theoretical value in controlling the concentrations of various chemical substances.
{"title":"Extended Hybrid Controller Design of Bifurcation in a Delayed Chemostat Model","authors":"Changjin Xu, Qing Cui, Zixin Liu, Yuanlu Pan, Xiaohan Cui, Wei-Bo Ou, Mati ur Rahman, Muhammad Farman, Shabir Ahmad, A. Zeb","doi":"10.46793/match.90-3.609x","DOIUrl":"https://doi.org/10.46793/match.90-3.609x","url":null,"abstract":"Fractional-order differential models plays a pivotal role in depicting the relationship among concentration changes of various chemical substances in chemistry. In this current study, we will explore the dynamics of a delayed chemostat model. First of all, we prove that the solution of the delayed chemostat model exists and is unique by virtue of fixed point theorem. Secondly, we demonstrate that the solution of the delayed chemostat model is non-negative by applying some suitable inequality strategies. Thirdly, the boundedness of the solution to the delayed chemostat model is explored via constructing a reasonable function. Fourthly, the Hopf bifurcation and stability of the delayed chemostat model are dealt with by exploiting the stability criterion and bifurcation theory on fractional dynamical system. Fifthly, the stability domain and Hopf bifurcation of the delayed chemostat model are resoundingly controlled by making use of an extended hybrid controller. Sixthly, the stability domain and Hopf bifurcation of the delayed chemostat model are effectively adjusted by making use of an another extended hybrid controller. The role of delay in this chemostat model is revealed. Seventhly, software experiments are given to illustrate the rightness of the gained key conclusions. The acquired outcomes of this work are perfectly innovative and have crucial theoretical value in controlling the concentrations of various chemical substances.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87578371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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