{"title":"A novel controllability analysis of impulsive fractional linear time invariant systems with state delay and distributed delays in control","authors":"B. Vadivoo, R. Raja, R. Agarwal, G. Rajchaki","doi":"10.5890/DNC.2018.09.006","DOIUrl":"https://doi.org/10.5890/DNC.2018.09.006","url":null,"abstract":"","PeriodicalId":296600,"journal":{"name":"The interdisciplinary journal of Discontinuity, Nonlinearity and Complexity","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129930780","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 consider a general first order scalar difference equation with and without Allee effect. The model without Allee effect represents asexual reproduction of a species while the model including Allee effect represents sexual reproduction. We analyze global stabilities of both models analytically and compare the results obtained. Numerical simulations are included to support the analytical results. We conclude that Allee effect decreases global stability of a nonnegative fixed point of the model. This result is different from the local stability behavior of the same fixed point of the model.
{"title":"Global Stability Analysis of a General Scalar Difference Equation","authors":"H. Merdan, Ö. Gümüs, Gamzegul Karahisarli","doi":"10.5890/dnc.2018.09.001","DOIUrl":"https://doi.org/10.5890/dnc.2018.09.001","url":null,"abstract":"We consider a general first order scalar difference equation with and without Allee effect. The model without Allee effect represents asexual reproduction of a species while the model including Allee effect represents sexual reproduction. We analyze global stabilities of both models analytically and compare the results obtained. Numerical simulations are included to support the analytical results. We conclude that Allee effect decreases global stability of a nonnegative fixed point of the model. This result is different from the local stability behavior of the same fixed point of the model.","PeriodicalId":296600,"journal":{"name":"The interdisciplinary journal of Discontinuity, Nonlinearity and Complexity","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115303646","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":"Asymptotic Stability of Caputo Fractional Singular Differential Systems with Multiple Delays","authors":"S. Priyadharsini, V. Govindaraj","doi":"10.5890/DNC.2018.09.003","DOIUrl":"https://doi.org/10.5890/DNC.2018.09.003","url":null,"abstract":"","PeriodicalId":296600,"journal":{"name":"The interdisciplinary journal of Discontinuity, Nonlinearity and Complexity","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134243298","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":"Van der Pol Oscillators Generated from Grazing Dynamics","authors":"M. Akhmet, A. Kıvılcım","doi":"10.5890/DNC.2018.09.005","DOIUrl":"https://doi.org/10.5890/DNC.2018.09.005","url":null,"abstract":"","PeriodicalId":296600,"journal":{"name":"The interdisciplinary journal of Discontinuity, Nonlinearity and Complexity","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123554755","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":"Nonlinear Modifications of Perturbation Theory with Some Examples of Applications to Complex System Analysis","authors":"V. Uchaikin, V. A. Litvinov, E. V. Kozhemjakina","doi":"10.5890/DNC.2018.09.009","DOIUrl":"https://doi.org/10.5890/DNC.2018.09.009","url":null,"abstract":"","PeriodicalId":296600,"journal":{"name":"The interdisciplinary journal of Discontinuity, Nonlinearity and Complexity","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115072340","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":"Stability of Fractional Differential Equations without Singular Kernal","authors":"S. Harikrishnan, K. Kanagarajan, D. Vivek","doi":"10.5890/dnc.2018.09.004","DOIUrl":"https://doi.org/10.5890/dnc.2018.09.004","url":null,"abstract":"","PeriodicalId":296600,"journal":{"name":"The interdisciplinary journal of Discontinuity, Nonlinearity and Complexity","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125206585","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":"Approximate Controllability Results for Impulsive Partial Functional Nonlocal Integro-differential Evolution Systems through Resolvent Operators","authors":"M. Nagaraj, S. Suganya, D. Baleanu, M. Arjunan","doi":"10.5890/DNC.2018.09.008","DOIUrl":"https://doi.org/10.5890/DNC.2018.09.008","url":null,"abstract":"","PeriodicalId":296600,"journal":{"name":"The interdisciplinary journal of Discontinuity, Nonlinearity and Complexity","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130163670","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 prove global existence and uniqueness of strong solutions for the SchrödingerPoisson system in the repulsive Coulomb case with relativistic, magnetic kinetic energy.
{"title":"On the Well-posedness of the Magnetic, Semi-relativistic Schrodinger-Poisson System","authors":"V. Vougalter","doi":"10.5890/dnc.2018.09.002","DOIUrl":"https://doi.org/10.5890/dnc.2018.09.002","url":null,"abstract":"We prove global existence and uniqueness of strong solutions for the SchrödingerPoisson system in the repulsive Coulomb case with relativistic, magnetic kinetic energy.","PeriodicalId":296600,"journal":{"name":"The interdisciplinary journal of Discontinuity, Nonlinearity and Complexity","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123911547","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 paper considers impulsive systems with singularities. The main novelty of the present research is that impulses (impulsive functions) are singular. This is beside singularity of differential equations. The Lyapunov second method is applied to proof the main theorems. Illustrative examples with simulations are given to support the theoretical results.
{"title":"Tikhonov theorem for differential equations with singular impulses","authors":"M. Akhmet, S. cCaug","doi":"10.5890/dnc.2018.09.007","DOIUrl":"https://doi.org/10.5890/dnc.2018.09.007","url":null,"abstract":"The paper considers impulsive systems with singularities. The main novelty of the present research is that impulses (impulsive functions) are singular. This is beside singularity of differential equations. The Lyapunov second method is applied to proof the main theorems. Illustrative examples with simulations are given to support the theoretical results.","PeriodicalId":296600,"journal":{"name":"The interdisciplinary journal of Discontinuity, Nonlinearity and Complexity","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121596567","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":"Degree OF Approximation of Functions f ( x , y ) by Double Hausdorff Matrix Summability Method","authors":"Abhishek Mishra, V. Mishra","doi":"10.5890/dnc.2022.09.014","DOIUrl":"https://doi.org/10.5890/dnc.2022.09.014","url":null,"abstract":"","PeriodicalId":296600,"journal":{"name":"The interdisciplinary journal of Discontinuity, Nonlinearity and Complexity","volume":"316 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121480907","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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