Research ArticleOpen AccessGoogle Scholar indexed
Theoretically Expected Phase Portrait of an Initial Value Problem with Periodic Piecewise Continuous Functions
Independent Researcher, Luque, Paraguay
- 1 Independent Researcher, Luque, Paraguay
International Journal of Modern Nonlinear Theory and Application·Volume 13 (2024)·Pages 29–44·Published 30 September 2024·DOI10.4236/ijmnta.2024.133003
Copy link · social · email
Abstract
This work predicts theoretically the phase portrait including the existence and uniqueness of ω -limit cycle for an initial value problem y ( 0 ) = y 0 with an ordinary differential equation y ′ + p y = f in which p and f are L -periodic piecewise continuous functions.
KeywordsOrdinary Linear Nonhomogeneous Differential EquationOne-Sided Limits
- Brin, M. and Stuck, G. (2004) Introduction to Dynamical Systems. Cambridge University Press.
- Hirsch, M.W. and Smale, S. (2013) Differential Equations, Dynamical System, and an Introduction to Chaos. Elsevier Inc.
- Ma, S. and Hogan, S.J. (2024) Generalized Hopf Bifurcation in a Delay Model of Neutrophil Cells Model. International Journal of Modern Nonlinear Theory and Application , 13, 11-28. https://doi.org/10.4236/ijmnta.2024.132002
- Brauer, F. and Nohel, J.A. (1969) The Qualitative Theory of Ordinary Differential Equations. An Introduction. Dover Publications, Inc.
- Birnir, B. (2008) Dynamical Systems Theory.
- Boyce, W.E. and Di Prima, R.C. (2019) Elementary Differential Equations and Boundary Value Problem. 9th Edition, John Wiley & Sons, Inc.
- López, A.M. (2018) Different Dynamical Aspects of Lorenz System. Trebal Final de Grau. Universita de Barcelona.
- Knill, O. (2005) Dynamical Systems. Harvard University. https://abel.math.harvard.edu/archive/118r_spring_05/handouts/text.pdf
- Yu, P.Y. and Craciun, G. (2018) Mathematical Analysis of Chemical Reaction Systems. Israel Journal of Chemistry , 58, 733-741. https://doi.org/10.1002/ijch.201800003
- Teramoto, H., Toda, M. and Komatsuzaki, T. (2015) Understandings of Chemical Reaction Dynamics in Terms of Dynamical Systems Theory. AIP Conference Proceedings , 1702, Article ID: 090042. https://doi.org/10.1063/1.4938850
- Alligood, K.T., Sauer, T.D. and Yorke, J.A. (1996) Chaos: An Introduction to Dynamical Systems. Springer Verlag.
- Zill, D.G. (2012) A First Course in Differential Equations with Modelling Applications. 10th Edition, Brooks/Cole Cengage Learning.
- Mwangi, S.M.N., Kitetu, V.M. and Okwany, I.O. (2024) Mathematical Modeling of HIV Investigating the Effect of Inconsistent Treatment. Journal of Applied Mathematics and Physics , 12, 1063-1078. https://doi.org/10.4236/jamp.2024.124066
- Shone, R. (2002) Economic Dynamics. Phase Diagrams and Their Economic Application. 2nd Edition, Cambridge University Press.
- Philos, C.G. (1991) Oscillations of First Order Linear Retarded Differential Equations. Journal of Mathematical Analysis and Applications , 157, 17-33. https://doi.org/10.1016/0022-247x(91)90134-l