In this paper, modification of double Laplace decomposition method is proposed for the analytical approximation solution of a coupled system of Burgers equation with appropriate initial conditions. Some examples are given to support the validity and applicability of the presented method.
{"title":"A note on a singular coupled Burgers equation and double Laplace transform method","authors":"H. Eltayeb, S. Mesloub, A. Kılıçman","doi":"10.22436/JNSA.011.05.05","DOIUrl":"https://doi.org/10.22436/JNSA.011.05.05","url":null,"abstract":"In this paper, modification of double Laplace decomposition method is proposed for the analytical approximation solution of a coupled system of Burgers equation with appropriate initial conditions. Some examples are given to support the validity and applicability of the presented method.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"128 1","pages":"635-643"},"PeriodicalIF":0.0,"publicationDate":"2018-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73066488","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}
This paper mainly deals with the stability of delayed neural networks with time-varying impulses, in which both stabilizing and destabilizing impulses are considered. By means of the comparison principle, the average impulsive interval and the Lyapunov function approach, sufficient conditions are obtained to ensure that the considered impulsive delayed neural network is exponentially stable. Different from existing results on stability of impulsive systems with average impulsive approach, it is assumed that impulsive strengths of stabilizing and destabilizing impulses take values from two finite states, and a new definition of impulsive strength-dependent average impulsive interval is proposed to characterize the impulsive sequence. The characteristics of the proposed impulsive strength-dependent average impulsive interval is that each impulsive strength has its own average impulsive interval and therefore the proposed impulsive strength-dependent average impulsive interval is more applicable than the average impulsive interval. Simulation examples are given to show the validity and potential advantages of the developed results.
{"title":"Stability of delayed neural networks with impulsive strength-dependent average impulsive intervals","authors":"Huan Zhang, Wenbing Zhang, Z. Li","doi":"10.22436/JNSA.011.05.02","DOIUrl":"https://doi.org/10.22436/JNSA.011.05.02","url":null,"abstract":"This paper mainly deals with the stability of delayed neural networks with time-varying impulses, in which both stabilizing and destabilizing impulses are considered. By means of the comparison principle, the average impulsive interval and the Lyapunov function approach, sufficient conditions are obtained to ensure that the considered impulsive delayed neural network is exponentially stable. Different from existing results on stability of impulsive systems with average impulsive approach, it is assumed that impulsive strengths of stabilizing and destabilizing impulses take values from two finite states, and a new definition of impulsive strength-dependent average impulsive interval is proposed to characterize the impulsive sequence. The characteristics of the proposed impulsive strength-dependent average impulsive interval is that each impulsive strength has its own average impulsive interval and therefore the proposed impulsive strength-dependent average impulsive interval is more applicable than the average impulsive interval. Simulation examples are given to show the validity and potential advantages of the developed results.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"96 1","pages":"602-612"},"PeriodicalIF":0.0,"publicationDate":"2018-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74127591","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}
{"title":"A generalization of Elsayed's solution to the difference equation x n + 1 = x n − 5 − 1 + x n − 2 x n − 5","authors":"M. Folly-Gbetoula, D. Nyirenda","doi":"10.22436/JNSA.011.05.03","DOIUrl":"https://doi.org/10.22436/JNSA.011.05.03","url":null,"abstract":"","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"59 1","pages":"613-623"},"PeriodicalIF":0.0,"publicationDate":"2018-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79427243","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}
A derangement is a permutation that has no fixed point and the derangement number dm is the number of fixed pointfree permutations on an m element set. A generalization of the derangement numbers are the r-derangement numbers and their natural companions are the r-derangement polynomials. In this paper we will study three types of sums of products of r-derangement functions and find Fourier series expansions of them. In addition, we will express them in terms of Bernoulli functions. As immediate corollaries to this, we will be able to express the corresponding three types of polynomials as linear combinations of Bernoulli polynomials.
{"title":"Fourier series of sums of products of r-derangement functions","authors":"Taekyun Kim, Dae San Kim, Huck-In Kwon, L. Jang","doi":"10.22436/JNSA.011.04.12","DOIUrl":"https://doi.org/10.22436/JNSA.011.04.12","url":null,"abstract":"A derangement is a permutation that has no fixed point and the derangement number dm is the number of fixed pointfree permutations on an m element set. A generalization of the derangement numbers are the r-derangement numbers and their natural companions are the r-derangement polynomials. In this paper we will study three types of sums of products of r-derangement functions and find Fourier series expansions of them. In addition, we will express them in terms of Bernoulli functions. As immediate corollaries to this, we will be able to express the corresponding three types of polynomials as linear combinations of Bernoulli polynomials.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"79 1","pages":"575-590"},"PeriodicalIF":0.0,"publicationDate":"2018-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86663565","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}
In this paper, we consider the following nonlinear Schrödinger-Poisson system { −∆u+ V(x)u+K(x)φu = f(x,u), x ∈ R3, −∆φ = K(x)u2, x ∈ R3, where V ,K ∈ L∞(R3) and f : R3 ×R→ R is continuous. We prove that the problem has a nontrivial solution under asymptotically periodic case of V ,K, and f at infinity. Moreover, the nonlinear term f does not satisfy any monotone condition.
{"title":"Existence of solutions for Schrödinger-Poisson system with asymptotically periodic terms","authors":"Da-Bin Wang, Lu-Ping Ma, Wen Guan, Hong-Mei Wu","doi":"10.22436/jnsa.011.05.01","DOIUrl":"https://doi.org/10.22436/jnsa.011.05.01","url":null,"abstract":"In this paper, we consider the following nonlinear Schrödinger-Poisson system { −∆u+ V(x)u+K(x)φu = f(x,u), x ∈ R3, −∆φ = K(x)u2, x ∈ R3, where V ,K ∈ L∞(R3) and f : R3 ×R→ R is continuous. We prove that the problem has a nontrivial solution under asymptotically periodic case of V ,K, and f at infinity. Moreover, the nonlinear term f does not satisfy any monotone condition.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"43 1","pages":"591-601"},"PeriodicalIF":0.0,"publicationDate":"2018-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76586697","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}
The problem of guaranteed cost control for exponential function projective synchronization (EFPS) for complex dynamical networks with mixed time-varying delays and hybrid uncertainties asymmetric coupling delays, composing of state coupling, time-varying delay coupling, and distributed time-varying delay coupling, is investigated. In this work, the uncertainties coupling configuration matrix need not be symmetric or irreducible. The guaranteed cost control for EFPS of delayed complex dynamical networks is considered via hybrid control with nonlinear and mixed linear feedback controls, including error linear term, time-varying delay error linear term, and distributed time-varying delay error linear term. Based on the construction of improved Lyapunov-Krasovskii functional with the technique of dealing with some integral terms, the new sufficient conditions for the existence of the optimal guaranteed cost control laws are presented in terms of linear matrix inequalities (LMIs). The obtained LMIs can be efficiently solved by standard convex optimization algorithms. Moreover, numerical examples are given to demonstrate the effectiveness of proposed guaranteed cost control for EFPS. The results in this article generalize and improve the corresponding results of the recent works.
{"title":"Guaranteed cost control of exponential function projective synchronization of delayed complex dynamical networks with hybrid uncertainties asymmetric coupling delays","authors":"W. Weera, T. Botmart, P. Niamsup, N. Yotha","doi":"10.22436/jnsa.011.04.11","DOIUrl":"https://doi.org/10.22436/jnsa.011.04.11","url":null,"abstract":"The problem of guaranteed cost control for exponential function projective synchronization (EFPS) for complex dynamical networks with mixed time-varying delays and hybrid uncertainties asymmetric coupling delays, composing of state coupling, time-varying delay coupling, and distributed time-varying delay coupling, is investigated. In this work, the uncertainties coupling configuration matrix need not be symmetric or irreducible. The guaranteed cost control for EFPS of delayed complex dynamical networks is considered via hybrid control with nonlinear and mixed linear feedback controls, including error linear term, time-varying delay error linear term, and distributed time-varying delay error linear term. Based on the construction of improved Lyapunov-Krasovskii functional with the technique of dealing with some integral terms, the new sufficient conditions for the existence of the optimal guaranteed cost control laws are presented in terms of linear matrix inequalities (LMIs). The obtained LMIs can be efficiently solved by standard convex optimization algorithms. Moreover, numerical examples are given to demonstrate the effectiveness of proposed guaranteed cost control for EFPS. The results in this article generalize and improve the corresponding results of the recent works.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"31 1","pages":"550-574"},"PeriodicalIF":0.0,"publicationDate":"2018-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91524455","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}
In 2013, the mixed complex intersection bodies of star bodies was introduced. Following this, in the paper, we establish Aleksandrov-Fenchel and Brunn-Minkowski type inequalities for the mixed complex intersection bodies, which in special case yield some of the recent results.
{"title":"On mixed complex intersection bodies","authors":"Chang-Jian Zhao","doi":"10.22436/JNSA.011.04.10","DOIUrl":"https://doi.org/10.22436/JNSA.011.04.10","url":null,"abstract":"In 2013, the mixed complex intersection bodies of star bodies was introduced. Following this, in the paper, we establish Aleksandrov-Fenchel and Brunn-Minkowski type inequalities for the mixed complex intersection bodies, which in special case yield some of the recent results.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"59 1","pages":"541-549"},"PeriodicalIF":0.0,"publicationDate":"2018-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81799556","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}
An immunological model of HIV-1 infection that accounts for antiretroviral drug uptake via explicit compartments is considered. Different from traditional methods where the drug effects is modeled implicitly as a proportional inhibition of viral infection and production, in this paper, it is assumed that the CD4+ T cells can ’prey on’ the antiretroviral drugs and become the cells which cannot be infected or produce new virions. Drug dymamics is modeled applying impulsive differential equations. The basic reproductive number R0 is defined via the next infection operator. It is shown that with perfect adherence the virus can be eradicated permanently if R0 is less than unity, otherwise, the virus can persist by applying persistent theory. The effects of imperfect adherence are also explored. The results indicate that even for the same degree of adherence, different adherence patterns may lead to different therapy outcomes. In particular, for regular dosage missing, the more dosages are consecutively missed, the worse therapy outcomes will be.
{"title":"Viral dynamics of an HIV model with pulse antiretroviral therapy and adherence","authors":"Youping Yang","doi":"10.22436/jnsa.011.04.08","DOIUrl":"https://doi.org/10.22436/jnsa.011.04.08","url":null,"abstract":"An immunological model of HIV-1 infection that accounts for antiretroviral drug uptake via explicit compartments is considered. Different from traditional methods where the drug effects is modeled implicitly as a proportional inhibition of viral infection and production, in this paper, it is assumed that the CD4+ T cells can ’prey on’ the antiretroviral drugs and become the cells which cannot be infected or produce new virions. Drug dymamics is modeled applying impulsive differential equations. The basic reproductive number R0 is defined via the next infection operator. It is shown that with perfect adherence the virus can be eradicated permanently if R0 is less than unity, otherwise, the virus can persist by applying persistent theory. The effects of imperfect adherence are also explored. The results indicate that even for the same degree of adherence, different adherence patterns may lead to different therapy outcomes. In particular, for regular dosage missing, the more dosages are consecutively missed, the worse therapy outcomes will be.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"25 1","pages":"516-528"},"PeriodicalIF":0.0,"publicationDate":"2018-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78073419","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}
{"title":"Strong convergence of a new iterative algorithm for fixed points of asymptotically nonexpansive mappings","authors":"Yuanheng Wang, Jialei Feng","doi":"10.22436/jnsa.011.04.09","DOIUrl":"https://doi.org/10.22436/jnsa.011.04.09","url":null,"abstract":"","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"44 1","pages":"529-540"},"PeriodicalIF":0.0,"publicationDate":"2018-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83706985","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}
In this paper, we consider three types of functions given by products of Bernoulli and ordered Bell functions and derive their Fourier series expansions. In addition, we will express each of them in terms of Bernoulli functions.
{"title":"Fourier series of finite product of Bernoulli and ordered Bell functions","authors":"Taekyun Kim, Dae San Kim, D. V. Dolgy, J. Kwon","doi":"10.22436/JNSA.011.04.07","DOIUrl":"https://doi.org/10.22436/JNSA.011.04.07","url":null,"abstract":"In this paper, we consider three types of functions given by products of Bernoulli and ordered Bell functions and derive their Fourier series expansions. In addition, we will express each of them in terms of Bernoulli functions.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"13 1","pages":"500-515"},"PeriodicalIF":0.0,"publicationDate":"2018-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90314009","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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