. Of concern is a wave equation which takes into account a discrete time delay in the state itself (and not in its time derivative). It is also subject to impulses and a control given by a (cid:12)nite memory term. We prove the well-posedness and exponential stability of our system. Our stability result shows that the damping effect of the (cid:12)nite memory term is not destroyed neither by the impulses nor by the delay.
{"title":"Well-Posedness and Stability of a Retarded Impulsive Wave Equation with a Finite Memory","authors":"Aissa Guesmia, Nasser Eddine Tatar","doi":"10.46719/dsa2023.32.05","DOIUrl":"https://doi.org/10.46719/dsa2023.32.05","url":null,"abstract":". Of concern is a wave equation which takes into account a discrete time delay in the state itself (and not in its time derivative). It is also subject to impulses and a control given by a (cid:12)nite memory term. We prove the well-posedness and exponential stability of our system. Our stability result shows that the damping effect of the (cid:12)nite memory term is not destroyed neither by the impulses nor by the delay.","PeriodicalId":51019,"journal":{"name":"Dynamic Systems and Applications","volume":"284 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135715826","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}
. We estimate the drift in the semilinear SPDE by approximation by space and time discretization. We study the asymptotic properties of the approximate maximum likelihood estimators and also the rates of convergence. We also study parameter estimation in controlled semilinear SPDE.
{"title":"Approximate Maximum Likelihood Estimation in Semilinear SPDE","authors":"Jaya P. N Bishwal","doi":"10.46719/dsa2023.32.10","DOIUrl":"https://doi.org/10.46719/dsa2023.32.10","url":null,"abstract":". We estimate the drift in the semilinear SPDE by approximation by space and time discretization. We study the asymptotic properties of the approximate maximum likelihood estimators and also the rates of convergence. We also study parameter estimation in controlled semilinear SPDE.","PeriodicalId":51019,"journal":{"name":"Dynamic Systems and Applications","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135715830","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":"Larch Budmoth Interaction: Stability, Bifurcation and Chaos Control","authors":"E M Elsayed, Qamar Din","doi":"10.46719/dsa2023.32.12","DOIUrl":"https://doi.org/10.46719/dsa2023.32.12","url":null,"abstract":"","PeriodicalId":51019,"journal":{"name":"Dynamic Systems and Applications","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135715837","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}
Ayman M Mahmoud, Abd Elmotaleb A M A Elamin, Shiraz E A Elhussein, Mawadda E Eboelhasan
. In this study, we analyse the nonautonomous multi-delay stochastic Li´enard equation and develop sufficient conditions for the equation’s stability and boundedness. The Lyapunov functional (LF) technique is used as the primary instrument in the proofs and we extend and enhance some stability and boundedness conclusions from the literature through our work. Two examples are used to support the correctness and efficacy of the results as an application. Finally, using the Euler-Maruyama method (EM-method), numerical simulations are provided in the final part to illustrate the approximative numerical solutions for the Li´enard system under consideration.
{"title":"Some Qualitative Properties of Solutions For Multi-Delay Nonautonomous Stochastic Lienard Equation","authors":"Ayman M Mahmoud, Abd Elmotaleb A M A Elamin, Shiraz E A Elhussein, Mawadda E Eboelhasan","doi":"10.46719/dsa2023.32.06","DOIUrl":"https://doi.org/10.46719/dsa2023.32.06","url":null,"abstract":". In this study, we analyse the nonautonomous multi-delay stochastic Li´enard equation and develop sufficient conditions for the equation’s stability and boundedness. The Lyapunov functional (LF) technique is used as the primary instrument in the proofs and we extend and enhance some stability and boundedness conclusions from the literature through our work. Two examples are used to support the correctness and efficacy of the results as an application. Finally, using the Euler-Maruyama method (EM-method), numerical simulations are provided in the final part to illustrate the approximative numerical solutions for the Li´enard system under consideration.","PeriodicalId":51019,"journal":{"name":"Dynamic Systems and Applications","volume":"76 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135715829","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":"On Some Retarded Integral Inequalities of Gronwall Type: Application to Integral and Differential Equations","authors":"T Ghrissi, M A Hammamiy","doi":"10.46719/dsa2023.32.03","DOIUrl":"https://doi.org/10.46719/dsa2023.32.03","url":null,"abstract":"","PeriodicalId":51019,"journal":{"name":"Dynamic Systems and Applications","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135715821","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 : 2022-09-25DOI: 10.46719/dsa202231.03.04
S. Romaguera, P. Tirado
{"title":"Remarks on the Quasi-Metric Extension of the Meir-Keeler Fixed Point Theorem With an Application to D3-Systems","authors":"S. Romaguera, P. Tirado","doi":"10.46719/dsa202231.03.04","DOIUrl":"https://doi.org/10.46719/dsa202231.03.04","url":null,"abstract":"","PeriodicalId":51019,"journal":{"name":"Dynamic Systems and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45269504","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 : 2022-09-25DOI: 10.46719/dsa202231.03.03
R. P. Pant, R. Nikolić, M. Joshi
{"title":"A Caristi and Meir-Keeler Type Characterization of Completeness For Menger PM Spaces","authors":"R. P. Pant, R. Nikolić, M. Joshi","doi":"10.46719/dsa202231.03.03","DOIUrl":"https://doi.org/10.46719/dsa202231.03.03","url":null,"abstract":"","PeriodicalId":51019,"journal":{"name":"Dynamic Systems and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43621983","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 : 2022-09-25DOI: 10.46719/dsa202231.03.05
S. Romaguera, P. Tirado
{"title":"Showing the Existence and Uniqueness of Solution for Certain Rational Difference Equations by Means of a Fixed Point Theorem of Browder’s Type","authors":"S. Romaguera, P. Tirado","doi":"10.46719/dsa202231.03.05","DOIUrl":"https://doi.org/10.46719/dsa202231.03.05","url":null,"abstract":"","PeriodicalId":51019,"journal":{"name":"Dynamic Systems and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44909784","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 : 2022-09-25DOI: 10.46719/dsa202231.03.01
Junping Nan, Weimin Hu, You-Hui Su, Xiaoling Han
{"title":"Stability and Existence of Solutions For Fractional Differential System With p-Laplacian Operator on Star Graphs","authors":"Junping Nan, Weimin Hu, You-Hui Su, Xiaoling Han","doi":"10.46719/dsa202231.03.01","DOIUrl":"https://doi.org/10.46719/dsa202231.03.01","url":null,"abstract":"","PeriodicalId":51019,"journal":{"name":"Dynamic Systems and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47109869","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 : 2022-09-25DOI: 10.46719/dsa202231.03.02
O. Oyewole, A. Zaslavski, S. Reich
{"title":"A Fixed Point Theorem in Length Spaces","authors":"O. Oyewole, A. Zaslavski, S. Reich","doi":"10.46719/dsa202231.03.02","DOIUrl":"https://doi.org/10.46719/dsa202231.03.02","url":null,"abstract":"","PeriodicalId":51019,"journal":{"name":"Dynamic Systems and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49290266","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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