{"title":"Applications of Fixed Point Theorems to the Problem of the Equilibrium Strategy Existence Preservation in a Parametric Family of Antagonistic Games","authors":"Tatiana N Fomenko","doi":"10.46719/dsa2023.32.04","DOIUrl":"https://doi.org/10.46719/dsa2023.32.04","url":null,"abstract":"","PeriodicalId":51019,"journal":{"name":"Dynamic Systems and Applications","volume":"6 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":"135715832","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}
. Necessary and sufficient conditions for almost sure asymptotic stability of solutions of stochastic dynamical systems generated by linear and nonlinear, nonautonomous ordinary stochastic difference equations (SDE) in R 1
{"title":"A Martingale Approach to Asymptotic Stability Of Nonlinear Stochastic Difference Equations With Bounded Noise in R1","authors":"Alexandra Rodkina, Henri Schurz","doi":"10.46719/dsa2023.32.08","DOIUrl":"https://doi.org/10.46719/dsa2023.32.08","url":null,"abstract":". Necessary and sufficient conditions for almost sure asymptotic stability of solutions of stochastic dynamical systems generated by linear and nonlinear, nonautonomous ordinary stochastic difference equations (SDE) in R 1","PeriodicalId":51019,"journal":{"name":"Dynamic Systems and Applications","volume":"94 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":"135715836","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, the authors establish conditions for the existence of solutions to impulsive Caputo-Hadamard fractional differential equations with integral boundary conditions. The proofs make use of the Banach contraction theorem, Schauder’s fixed point theorem, and the nonlinear Leray-Schauder alternative. An example to illustrate the results is given.
{"title":"Existence Results for Impulsive Caputo-Hadamard Fractional Differential Equations with Integral Boundary Conditions","authors":"John R Graef, Samira Hamani","doi":"10.46719/dsa2023.32.01","DOIUrl":"https://doi.org/10.46719/dsa2023.32.01","url":null,"abstract":". In this paper, the authors establish conditions for the existence of solutions to impulsive Caputo-Hadamard fractional differential equations with integral boundary conditions. The proofs make use of the Banach contraction theorem, Schauder’s fixed point theorem, and the nonlinear Leray-Schauder alternative. An example to illustrate the results is given.","PeriodicalId":51019,"journal":{"name":"Dynamic Systems and Applications","volume":"13 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":"135715825","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}
K Suddalai Kannan, S M Abdul Kader, M V Sethumeenakshi, V Chinnathambi, S Rajasekar
. This paper highlights on the occurrence of vibrational resonance (VR), investigated in a double-well position-dependent mass (PDM)-Du–ng oscillator system driven by an amplitude modulated (AM) force. The AM force consists of one low-frequency ( ! ) component and two high-frequencies (› + ! ) and (› ¡ ! ) components with (› (cid:192) ! ). In the PDM-Du–ng oscillator with one low-frequency and one high-frequency forces, by applying a theoretical approach an analytical expression is obtained for the response amplitude at the low-frequency ( ! ). The system provides an interesting scenario where PDM function makes a signiflcant contribution to the occurrence of VR. We examine the role played by PDM parameters ( m 0 ; ‚ ) and force parameters ( g; !; ›) on VR. We show the enhanced response amplitude Q at the low-frequency ! , showing more number of resonance peaks, a non-decay of response amplitude and hysteresis and a jump phenomenon on the response amplitude curve due to the amplitude modulated force. Results of analytical investigations are validated and complemented by numerical simulation.
{"title":"Nonlinear Response of a Position Dependent Mass System Driven by an Amplitude Modulated Force","authors":"K Suddalai Kannan, S M Abdul Kader, M V Sethumeenakshi, V Chinnathambi, S Rajasekar","doi":"10.46719/dsa2023.32.02","DOIUrl":"https://doi.org/10.46719/dsa2023.32.02","url":null,"abstract":". This paper highlights on the occurrence of vibrational resonance (VR), investigated in a double-well position-dependent mass (PDM)-Du–ng oscillator system driven by an amplitude modulated (AM) force. The AM force consists of one low-frequency ( ! ) component and two high-frequencies (› + ! ) and (› ¡ ! ) components with (› (cid:192) ! ). In the PDM-Du–ng oscillator with one low-frequency and one high-frequency forces, by applying a theoretical approach an analytical expression is obtained for the response amplitude at the low-frequency ( ! ). The system provides an interesting scenario where PDM function makes a signiflcant contribution to the occurrence of VR. We examine the role played by PDM parameters ( m 0 ; ‚ ) and force parameters ( g; !; ›) on VR. We show the enhanced response amplitude Q at the low-frequency ! , showing more number of resonance peaks, a non-decay of response amplitude and hysteresis and a jump phenomenon on the response amplitude curve due to the amplitude modulated force. Results of analytical investigations are validated and complemented by numerical simulation.","PeriodicalId":51019,"journal":{"name":"Dynamic Systems and Applications","volume":"12 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":"135715835","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 a given in(cid:12)nite series in x of the form y ( x ) = ∑ 1 k =0 b k x k expressed formally also by an in(cid:12)nite product as y ( x ) = (cid:5) 1 k =1 (1 (cid:0) xa k ) into real positive zeros a i ; i = 1 ; 2 ; : : : ; 1 forming a strictly increasing sequence. For consideration of polynomials of degree n , we replace suitably 1 by n . Using the known formal solution of a second linear differential y " = f ( x ) y; y (0) = y 0 ; y ′ (0) = y ′ 0 in the form y ( x ) = ∑ 1 k =0 d k x k , we demonstrate that the above in(cid:12)nite product form of y ( x ) yields the set of in(cid:12)nite equations of the form for a suitable f ( x ). ∑ 1 k =1 ( a k ) (cid:0) p = c p , p = 1 ; 2 ; : : : ; 1 with c ′ k s depending on f ( x ), its derivarives at x = 0 and b ′ k s. Recognizing the in(cid:12)nite matrix as the in(cid:12)nite Vandermonde matrix, some bounds for the zeros are given.
{"title":"On Zeros of Polynomials and Infinite Series With Some Bounds","authors":"P. N Shivakumar, Yang Zhang, Ashish Gupta","doi":"10.46719/dsa2023.32.09","DOIUrl":"https://doi.org/10.46719/dsa2023.32.09","url":null,"abstract":". In this paper, we consider a given in(cid:12)nite series in x of the form y ( x ) = ∑ 1 k =0 b k x k expressed formally also by an in(cid:12)nite product as y ( x ) = (cid:5) 1 k =1 (1 (cid:0) xa k ) into real positive zeros a i ; i = 1 ; 2 ; : : : ; 1 forming a strictly increasing sequence. For consideration of polynomials of degree n , we replace suitably 1 by n . Using the known formal solution of a second linear differential y \" = f ( x ) y; y (0) = y 0 ; y ′ (0) = y ′ 0 in the form y ( x ) = ∑ 1 k =0 d k x k , we demonstrate that the above in(cid:12)nite product form of y ( x ) yields the set of in(cid:12)nite equations of the form for a suitable f ( x ). ∑ 1 k =1 ( a k ) (cid:0) p = c p , p = 1 ; 2 ; : : : ; 1 with c ′ k s depending on f ( x ), its derivarives at x = 0 and b ′ k s. Recognizing the in(cid:12)nite matrix as the in(cid:12)nite Vandermonde matrix, some bounds for the zeros are given.","PeriodicalId":51019,"journal":{"name":"Dynamic Systems and Applications","volume":"12 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":"135715820","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":"Multiple Solutions of a Discrete Nonlinear Boundary Value Problem Involving p(k)-Laplace Kirchhoff Type Operator","authors":"Brahim Moussa, Ismael Nyanquini, Stanislas Ouaro","doi":"10.46719/dsa2023.32.13","DOIUrl":"https://doi.org/10.46719/dsa2023.32.13","url":null,"abstract":"","PeriodicalId":51019,"journal":{"name":"Dynamic Systems and Applications","volume":"28 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":"135715823","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}
Richard Avery, Douglas R Anderson, Johnny Henderson
{"title":"Decomposing a Conjugate Fixed-Point Problem into Multiple Fixed-Point Problems","authors":"Richard Avery, Douglas R Anderson, Johnny Henderson","doi":"10.46719/dsa2023.32.14","DOIUrl":"https://doi.org/10.46719/dsa2023.32.14","url":null,"abstract":"","PeriodicalId":51019,"journal":{"name":"Dynamic Systems and Applications","volume":"16 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":"135715824","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 present extended and improved results on the existence of solutions for the one-dimensional p -Laplacian impulsive differential equation with nonlinear Stieltjes integral boundary conditions, where the nonlinearity is a a
{"title":"Existence of Solutions for the One-Dimensional Fourth-Order p-Laplacian Impulsive Differential Equation Involving Nonlinear Stieltjes Integral Boundary Conditions","authors":"Yan Sun","doi":"10.46719/dsa2023.32.07","DOIUrl":"https://doi.org/10.46719/dsa2023.32.07","url":null,"abstract":". In this paper, we present extended and improved results on the existence of solutions for the one-dimensional p -Laplacian impulsive differential equation with nonlinear Stieltjes integral boundary conditions, where the nonlinearity is a a","PeriodicalId":51019,"journal":{"name":"Dynamic Systems and Applications","volume":"46 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":"135715827","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":"Phase Portraits of The Complex Riccati Equation With Constant Coefficients","authors":"Jaume Llibre, Claudia Valls","doi":"10.46719/dsa2023.32.11","DOIUrl":"https://doi.org/10.46719/dsa2023.32.11","url":null,"abstract":"","PeriodicalId":51019,"journal":{"name":"Dynamic Systems and Applications","volume":"410 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":"135715822","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":"Modeling Covid-19 Epidemic with Quarantine and Lockdown and Analysis","authors":"N Begashaw, Gurcan Comert, N G Medhin","doi":"10.46719/dsa2023.32.15","DOIUrl":"https://doi.org/10.46719/dsa2023.32.15","url":null,"abstract":"","PeriodicalId":51019,"journal":{"name":"Dynamic Systems and Applications","volume":"10 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":"135715828","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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