Pub Date : 2020-03-18DOI: 10.1504/ijdsde.2020.106027
M. Agaoglou, Michal Feckan, P. Angeliki, Panagiotidou
In this work we study the existence and uniqueness of (ω, c)-periodic solutions for semilinear evolution equations in complex Banach spaces.
本文研究了复Banach空间中半线性演化方程(ω， c)-周期解的存在唯一性。
{"title":"Existence and uniqueness of (ω,c)-periodic solutions of semilinear evolution equations","authors":"M. Agaoglou, Michal Feckan, P. Angeliki, Panagiotidou","doi":"10.1504/ijdsde.2020.106027","DOIUrl":"https://doi.org/10.1504/ijdsde.2020.106027","url":null,"abstract":"In this work we study the existence and uniqueness of (ω, c)-periodic solutions for semilinear evolution equations in complex Banach spaces.","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41815612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-03-18DOI: 10.1504/ijdsde.2020.106026
Yusen Wu, Laigang Guo
This paper identifies rough center for a Lotka-Volterra system, a 3-dimensional quadratic polynomial differential system with four parameters h, n, λ, μ. The known work shows the appearance of four limit cycles, but centre condition is not determined. In this paper, we verify the existence of at least four limit cycles in the positive equilibrium due to Hopf bifurcation by computing normal forms. Furthermore, by applying algorithms of computational commutative algebra we find Darboux polynomial and give a centre manifold in closed form globally, showing that the positive equilibrium of centre-focus is actually a rough center on a centre manifold.
{"title":"Rough center in a 3-dimensional Lotka-Volterra system","authors":"Yusen Wu, Laigang Guo","doi":"10.1504/ijdsde.2020.106026","DOIUrl":"https://doi.org/10.1504/ijdsde.2020.106026","url":null,"abstract":"This paper identifies rough center for a Lotka-Volterra system, a 3-dimensional quadratic polynomial differential system with four parameters h, n, λ, μ. The known work shows the appearance of four limit cycles, but centre condition is not determined. In this paper, we verify the existence of at least four limit cycles in the positive equilibrium due to Hopf bifurcation by computing normal forms. Furthermore, by applying algorithms of computational commutative algebra we find Darboux polynomial and give a centre manifold in closed form globally, showing that the positive equilibrium of centre-focus is actually a rough center on a centre manifold.","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1504/ijdsde.2020.106026","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48178419","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-02-05DOI: 10.1504/ijdsde.2020.10026687
Saranya Subbaiyan, A. Debbouche, Jinrong Wang
In this paper, we investigate approximate controllability of Hilfer fractional Sobolev type differential inclusions with nonlocal conditions. The main techniques rely on the fixed point theorem combined with the semigroup theory, fractional calculus and multivalued analysis. An example is provided to illustrate the obtained results.
{"title":"Approximate controllability of Hilfer fractional Sobolev type integrodifferential inclusions with nonlocal conditions","authors":"Saranya Subbaiyan, A. Debbouche, Jinrong Wang","doi":"10.1504/ijdsde.2020.10026687","DOIUrl":"https://doi.org/10.1504/ijdsde.2020.10026687","url":null,"abstract":"In this paper, we investigate approximate controllability of Hilfer fractional Sobolev type differential inclusions with nonlocal conditions. The main techniques rely on the fixed point theorem combined with the semigroup theory, fractional calculus and multivalued analysis. An example is provided to illustrate the obtained results.","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47431523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-02-05DOI: 10.1504/ijdsde.2020.10026682
Manjit Singh
The two-component Novikov equation is investigated for group classification and non-trivial local conservation laws. In addition to Lie group analysis, the existing classification of 4-dimensional Lie algebra is used to improve the classifications of Lie algebra of Novikov equations. Apart from this, the direct method is used in the construction of conservation laws using multipliers.
{"title":"On invariant analysis, group classification and conservation laws of two component Novikov equation","authors":"Manjit Singh","doi":"10.1504/ijdsde.2020.10026682","DOIUrl":"https://doi.org/10.1504/ijdsde.2020.10026682","url":null,"abstract":"The two-component Novikov equation is investigated for group classification and non-trivial local conservation laws. In addition to Lie group analysis, the existing classification of 4-dimensional Lie algebra is used to improve the classifications of Lie algebra of Novikov equations. Apart from this, the direct method is used in the construction of conservation laws using multipliers.","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45263412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-02-05DOI: 10.1504/ijdsde.2020.10026678
Tohid Kasbi, V. Roomi, A. J. Akbarfam
In this work a generalised Lienard type system will be considered. We study the problem whether all trajectories of this system intersect the vertical isocline, which is very important in the global asymptotic stability of the origin, oscillation theory, and existence of periodic solutions. Under quite general assumptions we obtain sufficient conditions which are very sharp. We present some new conditions under which the solutions of this system are oscillatory. Some examples are provided to illustrate our results.
{"title":"Some explicit oscillation results for the generalised Liénard type systems","authors":"Tohid Kasbi, V. Roomi, A. J. Akbarfam","doi":"10.1504/ijdsde.2020.10026678","DOIUrl":"https://doi.org/10.1504/ijdsde.2020.10026678","url":null,"abstract":"In this work a generalised Lienard type system will be considered. We study the problem whether all trajectories of this system intersect the vertical isocline, which is very important in the global asymptotic stability of the origin, oscillation theory, and existence of periodic solutions. Under quite general assumptions we obtain sufficient conditions which are very sharp. We present some new conditions under which the solutions of this system are oscillatory. Some examples are provided to illustrate our results.","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47292671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-02-05DOI: 10.1504/ijdsde.2020.10026688
A. Ehsani, F. Ghane, M. Zaj
We consider finitely generated semigroup actions on a compact manifold and discuss their ergodic properties. We introduce Markovian mostly expanding semigroups and show that each C1+α Markovian mostly expanding semigroup action is ergodic (with respect to the Lebesgue measure) whenever it is strongly tranitive. Moreover, it is proved that each Markovian mostly expanding semigroup is non uniformly expanding. Our approach provides a large class of non-uniformly expanding semigroups.
{"title":"On ergodicity of Markovian mostly expanding semi-group actions","authors":"A. Ehsani, F. Ghane, M. Zaj","doi":"10.1504/ijdsde.2020.10026688","DOIUrl":"https://doi.org/10.1504/ijdsde.2020.10026688","url":null,"abstract":"We consider finitely generated semigroup actions on a compact manifold and discuss their ergodic properties. We introduce Markovian mostly expanding semigroups and show that each C1+α Markovian mostly expanding semigroup action is ergodic (with respect to the Lebesgue measure) whenever it is strongly tranitive. Moreover, it is proved that each Markovian mostly expanding semigroup is non uniformly expanding. Our approach provides a large class of non-uniformly expanding semigroups.","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46642494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-02-05DOI: 10.1504/ijdsde.2020.10026685
H. Zeidabadi, M. Heidari
In this paper, a computational scheme for extracting approximate solutions of system of integral equations is proposed. For this purpose, by considering the variational form of the problem and using finite element method, the system of integral equations are reduced to a system of algebraic equations, that are solved by an efficient algorithm. Also, the existence and uniqueness of the system of integral equations are illustrated and the convergence of the approximate solution to the exact solution is investigated. Finally, the effectiveness of the proposed method is discussed by comparing with the results of the given approaches in Babolian and Mordad (2011) and Jafarian et al. (2013).
{"title":"A convergence computational scheme for system of integral equation using finite element method","authors":"H. Zeidabadi, M. Heidari","doi":"10.1504/ijdsde.2020.10026685","DOIUrl":"https://doi.org/10.1504/ijdsde.2020.10026685","url":null,"abstract":"In this paper, a computational scheme for extracting approximate solutions of system of integral equations is proposed. For this purpose, by considering the variational form of the problem and using finite element method, the system of integral equations are reduced to a system of algebraic equations, that are solved by an efficient algorithm. Also, the existence and uniqueness of the system of integral equations are illustrated and the convergence of the approximate solution to the exact solution is investigated. Finally, the effectiveness of the proposed method is discussed by comparing with the results of the given approaches in Babolian and Mordad (2011) and Jafarian et al. (2013).","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49668438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-02-05DOI: 10.1504/ijdsde.2020.10026680
Qingyue Zhang
Sampling theorems on a shift-invariant subspace are having a significant impact, since they avoid most of the problems associated with classical Shannon's theory. Vector sampling theorems on a shift-invariant subspace which are motivated by applications in multi-channel deconvolution and multi-source separation are active field of study. In this paper, we consider vector sampling theorems on a multivariate vector shift-invariant subspace. We give a multivariate vector sampling expansion on a multivariate vector shift-invariant subspace. Some equivalence conditions for the multivariate vector sampling expansion to hold are given. We also give several examples to illustrate the main result.
{"title":"Multivariate vector sampling expansion in shift-invariant subspaces","authors":"Qingyue Zhang","doi":"10.1504/ijdsde.2020.10026680","DOIUrl":"https://doi.org/10.1504/ijdsde.2020.10026680","url":null,"abstract":"Sampling theorems on a shift-invariant subspace are having a significant impact, since they avoid most of the problems associated with classical Shannon's theory. Vector sampling theorems on a shift-invariant subspace which are motivated by applications in multi-channel deconvolution and multi-source separation are active field of study. In this paper, we consider vector sampling theorems on a multivariate vector shift-invariant subspace. We give a multivariate vector sampling expansion on a multivariate vector shift-invariant subspace. Some equivalence conditions for the multivariate vector sampling expansion to hold are given. We also give several examples to illustrate the main result.","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":"10 1","pages":"19"},"PeriodicalIF":0.3,"publicationDate":"2020-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45219996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.1504/IJDSDE.2020.10035017
Changjin Xu
In this paper, we are concerned with a new fractional incommensurate order financial system which is a generalised version of the financial model investigated in earlier works. Designing a suitable time-delayed feedback controller, we have controlled the chaotic phenomenon of the fractional incommensurate order financial system. By analysing the characteristic equation of the involved financial system and regarding the delay as the bifurcation parameter, we establish a set of new sufficient conditions to guarantee the stability and the existence of Hopf bifurcation for fractional incommensurate order financial system. The study reveals that the delay and the fractional order have an important influence on the stability and Hopf bifurcation of considered financial system. Computer simulations are presented to illustrate the correctness of the theoretical results. The theoretical findings of this paper are new and have important meanings in dealing with the economic and financial problems.
{"title":"Delay feedback strategy for a fractional-order chaotic financial system","authors":"Changjin Xu","doi":"10.1504/IJDSDE.2020.10035017","DOIUrl":"https://doi.org/10.1504/IJDSDE.2020.10035017","url":null,"abstract":"In this paper, we are concerned with a new fractional incommensurate order financial system which is a generalised version of the financial model investigated in earlier works. Designing a suitable time-delayed feedback controller, we have controlled the chaotic phenomenon of the fractional incommensurate order financial system. By analysing the characteristic equation of the involved financial system and regarding the delay as the bifurcation parameter, we establish a set of new sufficient conditions to guarantee the stability and the existence of Hopf bifurcation for fractional incommensurate order financial system. The study reveals that the delay and the fractional order have an important influence on the stability and Hopf bifurcation of considered financial system. Computer simulations are presented to illustrate the correctness of the theoretical results. The theoretical findings of this paper are new and have important meanings in dealing with the economic and financial problems.","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66733549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.1504/ijdsde.2020.10033571
D. Kiouach, Y. Sabbar
{"title":"Global dynamics analysis of a stochastic SIRS epidemic model with vertical transmission and different periods of immunity","authors":"D. Kiouach, Y. Sabbar","doi":"10.1504/ijdsde.2020.10033571","DOIUrl":"https://doi.org/10.1504/ijdsde.2020.10033571","url":null,"abstract":"","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66733432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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