Pub Date : 2023-11-01DOI: 10.1007/s12346-023-00882-0
Joan C. Artés
Abstract This paper is part of a series of works whose ultimate goal is the complete classification of phase portraits of quadratic differential systems in the plane modulo limit cycles. It is estimated that the total number may be around 2000, so the work to find them all must be split in different papers in a systematic way so to assure the completeness of the study and also the non intersection among them. In this paper we classify the family of phase portraits possessing one finite saddle-node and a separatrix connection and determine that there are a minimum of 77 topologically different phase portraits plus at most 16 other phase portraits which we conjecture to be impossible. Along this paper we also deploy a mistake in the book (Artés et al. in Structurally unstable quadratic vector fields of codimension one, Birkhäuser/Springer, Cham, 2018) linked to a mistake in Reyn and Huang (Separatrix configuration of quadratic systems with finite multiplicity three and a $$M^0_{1,1}$$ M1,10 type of critical point at infinity. Report Technische Universiteit Delft, pp 95–115, 1995).
{"title":"Structurally Unstable Quadratic Vector Fields of Codimension Two: Families Possessing One Finite Saddle-Node and a Separatrix Connection","authors":"Joan C. Artés","doi":"10.1007/s12346-023-00882-0","DOIUrl":"https://doi.org/10.1007/s12346-023-00882-0","url":null,"abstract":"Abstract This paper is part of a series of works whose ultimate goal is the complete classification of phase portraits of quadratic differential systems in the plane modulo limit cycles. It is estimated that the total number may be around 2000, so the work to find them all must be split in different papers in a systematic way so to assure the completeness of the study and also the non intersection among them. In this paper we classify the family of phase portraits possessing one finite saddle-node and a separatrix connection and determine that there are a minimum of 77 topologically different phase portraits plus at most 16 other phase portraits which we conjecture to be impossible. Along this paper we also deploy a mistake in the book (Artés et al. in Structurally unstable quadratic vector fields of codimension one, Birkhäuser/Springer, Cham, 2018) linked to a mistake in Reyn and Huang (Separatrix configuration of quadratic systems with finite multiplicity three and a $$M^0_{1,1}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:mn>0</mml:mn> </mml:msubsup> </mml:math> type of critical point at infinity. Report Technische Universiteit Delft, pp 95–115, 1995).","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"58 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135270609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-01DOI: 10.1007/s12346-023-00894-w
Shahid Saifullah, Sumbel Shahid, Akbar Zada
{"title":"Analysis of Neutral Stochastic Fractional Differential Equations Involving Riemann–Liouville Fractional Derivative with Retarded and Advanced Arguments","authors":"Shahid Saifullah, Sumbel Shahid, Akbar Zada","doi":"10.1007/s12346-023-00894-w","DOIUrl":"https://doi.org/10.1007/s12346-023-00894-w","url":null,"abstract":"","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"38 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135271312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-01DOI: 10.1007/s12346-023-00895-9
Haide Gou, Yongxiang Li
{"title":"A Study on the Approximate Controllability of Damped Elastic Systems Using Sequence Method","authors":"Haide Gou, Yongxiang Li","doi":"10.1007/s12346-023-00895-9","DOIUrl":"https://doi.org/10.1007/s12346-023-00895-9","url":null,"abstract":"","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"244 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135320409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-31DOI: 10.1007/s12346-023-00887-9
Ting-ting Dai, Zeng-qi Ou, Ying Lv
{"title":"Normalized Solutions of Schrödinger Equations with Combined Nonlinearities","authors":"Ting-ting Dai, Zeng-qi Ou, Ying Lv","doi":"10.1007/s12346-023-00887-9","DOIUrl":"https://doi.org/10.1007/s12346-023-00887-9","url":null,"abstract":"","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135871737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-31DOI: 10.1007/s12346-023-00891-z
Mostafa Adimy, Abdennasser Chekroun, Charlotte Dugourd-Camus, Hanene Meghelli
We study the local and global asymptotic stability of the two steady-states, disease-free and endemic, of hybrid differential–difference SIR and SIS epidemic models with a nonlinear force of infection and a temporary phase of protection against the disease, e.g. by vaccination or medication. The initial model is an age-structured system that is reduced using the method of characteristic lines to a hybrid system, coupled between differential equations and a time continuous difference equation. We first prove that the solutions of the original system can be obtained from the reduced one. We then focus on the reduced system to obtain new results on the asymptotic stability of the two steady-states. We determine the local asymptotic stability of the two steady-states by studying the associated characteristic equation. We then discuss their global asymptotic stability in various situations (SIR, SIS, mass action, nonlinear force of infection), by constructing appropriate Lyapunov functions.
{"title":"Global Asymptotic Stability of a Hybrid Differential–Difference System Describing SIR and SIS Epidemic Models with a Protection Phase and a Nonlinear Force of Infection","authors":"Mostafa Adimy, Abdennasser Chekroun, Charlotte Dugourd-Camus, Hanene Meghelli","doi":"10.1007/s12346-023-00891-z","DOIUrl":"https://doi.org/10.1007/s12346-023-00891-z","url":null,"abstract":"We study the local and global asymptotic stability of the two steady-states, disease-free and endemic, of hybrid differential–difference SIR and SIS epidemic models with a nonlinear force of infection and a temporary phase of protection against the disease, e.g. by vaccination or medication. The initial model is an age-structured system that is reduced using the method of characteristic lines to a hybrid system, coupled between differential equations and a time continuous difference equation. We first prove that the solutions of the original system can be obtained from the reduced one. We then focus on the reduced system to obtain new results on the asymptotic stability of the two steady-states. We determine the local asymptotic stability of the two steady-states by studying the associated characteristic equation. We then discuss their global asymptotic stability in various situations (SIR, SIS, mass action, nonlinear force of infection), by constructing appropriate Lyapunov functions.","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"117 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135813263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-31DOI: 10.1007/s12346-023-00883-z
Lijun Zhang, M. M. Bhatti, Efstathios E. Michaelides, R. Ellahi
{"title":"Characterizing Quadratic Convection and Electromagnetically Induced Flow of Couple Stress Fluids in Microchannels","authors":"Lijun Zhang, M. M. Bhatti, Efstathios E. Michaelides, R. Ellahi","doi":"10.1007/s12346-023-00883-z","DOIUrl":"https://doi.org/10.1007/s12346-023-00883-z","url":null,"abstract":"","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"340 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135870283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-29DOI: 10.1007/s12346-023-00888-8
Lifeng Yin, Shuai Jiang
{"title":"Existence of Multiple Solutions for Elliptic Equations with Indefinite Potential","authors":"Lifeng Yin, Shuai Jiang","doi":"10.1007/s12346-023-00888-8","DOIUrl":"https://doi.org/10.1007/s12346-023-00888-8","url":null,"abstract":"","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"22 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136158023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-28DOI: 10.1007/s12346-023-00886-w
Divya Agrawal, Syed Abbas
{"title":"Existence of Periodic Solutions for a Class of Dynamic Equations with Multiple Time Varying Delays on Time Scales","authors":"Divya Agrawal, Syed Abbas","doi":"10.1007/s12346-023-00886-w","DOIUrl":"https://doi.org/10.1007/s12346-023-00886-w","url":null,"abstract":"","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"3 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136233049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-27DOI: 10.1007/s12346-023-00889-7
Manish Kumar, Rajesh Kumar Gupta
{"title":"Coupled Higgs Equation: Novel Solution via GSSE Method, Bifurcation and Chaotic Patterns and Series Solution via Symmetry","authors":"Manish Kumar, Rajesh Kumar Gupta","doi":"10.1007/s12346-023-00889-7","DOIUrl":"https://doi.org/10.1007/s12346-023-00889-7","url":null,"abstract":"","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136262341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-26DOI: 10.1007/s12346-023-00892-y
Rômulo M. Vermersch
{"title":"Measure-Theoretic Uniformly Positive Entropy on the Space of Probability Measures","authors":"Rômulo M. Vermersch","doi":"10.1007/s12346-023-00892-y","DOIUrl":"https://doi.org/10.1007/s12346-023-00892-y","url":null,"abstract":"","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"16 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136376343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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