Nonlinear Hybrid Continuous/Discrete-Time Models / Marat Akhmet (2011)  

Público ISBD Título : Nonlinear Hybrid Continuous/Discrete-Time Models Tipo de documento: documento electrónico Autores: Marat Akhmet ; SpringerLink (Online service) Editorial: Paris : Atlantis Press Fecha de publicación: 2011 Colección: Atlantis Studies in Mathematics for Engineering and Science, ISSN 1875-7642 num. 8 Número de páginas: XIII, 216 p Il.: online resource ISBN/ISSN/DL: 978-94-91216-03-9 Idioma : Inglés (eng) Palabras clave: Mathematics  Medicine  Differential  equations  Applied  mathematics  Engineering  Biomathematics  Ordinary  Equations  Applications  of  Physiological,  Cellular  and  Medical  Topics  Medicine/Public  Health,  general Clasificación: 51 Matemáticas Resumen: The book is mainly about hybrid systems with continuous/discrete-time dynamics. The major part of the book consists of the theory of equations with piece-wise constant argument of generalized type. The systems as well as technique of investigation were introduced by the author very recently. They both generalized known theory about differential equations with piece-wise constant argument, introduced by K. Cook and J. Wiener in the 1980s. Moreover, differential equations with fixed and variable moments of impulses are used to model real world problems. We consider models of neural networks, blood pressure distribution and a generalized model of the cardiac pacemaker. All the results of the manuscript have not been published in any book, yet. They are very recent and united with the presence of the continuous/discrete dynamics of time. It is of big interest for specialists in biology, medicine, engineering sciences, electronics. Theoretical aspects of the book meet very strong expectations of mathematicians who investigate differential equations with discontinuities of any type Nota de contenido: 1. Introduction -- 2. Linear and quasi-linear systems with piecewise constant argument -- 3. The reduction principle for systems with piecewise constant argument -- 4. The small parameter and differential equations with piecewise constant argument -- 5. Stability -- 6. The state-dependent piecewise constant argument -- 7. Almost periodic solutions -- 8. Stability of neural networks -- 9. The blood pressure distribution -- 10. Integrate-and-fire biological oscillators En línea: http://dx.doi.org/10.2991/978-94-91216-03-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33490 Nonlinear Hybrid Continuous/Discrete-Time Models [documento electrónico] / Marat Akhmet ; SpringerLink (Online service) . - Paris : Atlantis Press, 2011 . - XIII, 216 p : online resource. - (Atlantis Studies in Mathematics for Engineering and Science, ISSN 1875-7642; 8) . ISBN : 978-94-91216-03-9 Idioma : Inglés (eng) Palabras clave: Mathematics  Medicine  Differential  equations  Applied  mathematics  Engineering  Biomathematics  Ordinary  Equations  Applications  of  Physiological,  Cellular  and  Medical  Topics  Medicine/Public  Health,  general Clasificación: 51 Matemáticas Resumen: The book is mainly about hybrid systems with continuous/discrete-time dynamics. The major part of the book consists of the theory of equations with piece-wise constant argument of generalized type. The systems as well as technique of investigation were introduced by the author very recently. They both generalized known theory about differential equations with piece-wise constant argument, introduced by K. Cook and J. Wiener in the 1980s. Moreover, differential equations with fixed and variable moments of impulses are used to model real world problems. We consider models of neural networks, blood pressure distribution and a generalized model of the cardiac pacemaker. All the results of the manuscript have not been published in any book, yet. They are very recent and united with the presence of the continuous/discrete dynamics of time. It is of big interest for specialists in biology, medicine, engineering sciences, electronics. Theoretical aspects of the book meet very strong expectations of mathematicians who investigate differential equations with discontinuities of any type Nota de contenido: 1. Introduction -- 2. Linear and quasi-linear systems with piecewise constant argument -- 3. The reduction principle for systems with piecewise constant argument -- 4. The small parameter and differential equations with piecewise constant argument -- 5. Stability -- 6. The state-dependent piecewise constant argument -- 7. Almost periodic solutions -- 8. Stability of neural networks -- 9. The blood pressure distribution -- 10. Integrate-and-fire biological oscillators En línea: http://dx.doi.org/10.2991/978-94-91216-03-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33490

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Principles of Discontinuous Dynamical Systems / Marat Akhmet (2010)  

Público ISBD Título : Principles of Discontinuous Dynamical Systems Tipo de documento: documento electrónico Autores: Marat Akhmet ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2010 Otro editor: Imprint: Springer Número de páginas: XI, 176 p Il.: online resource ISBN/ISSN/DL: 978-1-4419-6581-3 Idioma : Inglés (eng) Palabras clave: Mathematics  Dynamics  Ergodic  theory  Differential  equations  Partial  differential  Dynamical  Systems  and  Theory  Ordinary  Equations Clasificación: 51 Matemáticas Resumen: Discontinuous dynamical systems have played an important role in both theory and applications during the last several decades. This is still an area of active research and techniques to make the applications more effective are an ongoing topic of interest. Principles of Discontinuous Dynamical Systems is devoted to the theory of differential equations with variable moments of impulses. It introduces a new strategy of implementing an equivalence to systems whose solutions have prescribed moments of impulses and utilizing special topologies in spaces of piecewise continuous functions. The achievements obtained on the basis of this approach are described in this book. The text progresses systematically, by covering preliminaries in the first four chapters. This is followed by more complex material and special topics such as Hopf bifurcation, Devaney's chaos, and the shadowing property are discussed in the last two chapters. This book is suitable for researchers and graduate students in mathematics and also in diverse areas such as biology, computer science, and engineering who deal with real world problems Nota de contenido: Description of the System with Fixed Moments of Impulses and Its Solutions -- Stability and Periodic Solutions of Systems with Fixed Moments of Impulses -- Basics of Linear Systems -- Nonautonomous Systems with Variable Moments of Impulses -- Differentiability Properties of Nonautonomous Systems -- Periodic Solutions of Nonlinear Systems -- Discontinuous Dynamical Systems -- Perturbations and Hopf Bifurcation of a Discontinuous Limit Cycle -- Chaos and Shadowing En línea: http://dx.doi.org/10.1007/978-1-4419-6581-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33633 Principles of Discontinuous Dynamical Systems [documento electrónico] / Marat Akhmet ; SpringerLink (Online service) . - New York, NY : Springer New York : Imprint: Springer, 2010 . - XI, 176 p : online resource. ISBN : 978-1-4419-6581-3 Idioma : Inglés (eng) Palabras clave: Mathematics  Dynamics  Ergodic  theory  Differential  equations  Partial  differential  Dynamical  Systems  and  Theory  Ordinary  Equations Clasificación: 51 Matemáticas Resumen: Discontinuous dynamical systems have played an important role in both theory and applications during the last several decades. This is still an area of active research and techniques to make the applications more effective are an ongoing topic of interest. Principles of Discontinuous Dynamical Systems is devoted to the theory of differential equations with variable moments of impulses. It introduces a new strategy of implementing an equivalence to systems whose solutions have prescribed moments of impulses and utilizing special topologies in spaces of piecewise continuous functions. The achievements obtained on the basis of this approach are described in this book. The text progresses systematically, by covering preliminaries in the first four chapters. This is followed by more complex material and special topics such as Hopf bifurcation, Devaney's chaos, and the shadowing property are discussed in the last two chapters. This book is suitable for researchers and graduate students in mathematics and also in diverse areas such as biology, computer science, and engineering who deal with real world problems Nota de contenido: Description of the System with Fixed Moments of Impulses and Its Solutions -- Stability and Periodic Solutions of Systems with Fixed Moments of Impulses -- Basics of Linear Systems -- Nonautonomous Systems with Variable Moments of Impulses -- Differentiability Properties of Nonautonomous Systems -- Periodic Solutions of Nonlinear Systems -- Discontinuous Dynamical Systems -- Perturbations and Hopf Bifurcation of a Discontinuous Limit Cycle -- Chaos and Shadowing En línea: http://dx.doi.org/10.1007/978-1-4419-6581-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33633

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