Ebook: Nonlinear Hybrid Continuous/Discrete-Time Models

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.

---

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.

---

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.
Content:
Front Matter....Pages i-xiii
Introduction....Pages 1-15
Linear and Quasi-Linear Systems with Piecewise Constant Argument....Pages 17-32
The Reduction Principle for Systems with Piecewise Constant Argument....Pages 33-48
The Small Parameter and Differential Equations with Piecewise Constant Argument....Pages 49-69
Stability....Pages 71-88
The State-Dependent Piecewise Constant Argument....Pages 89-104
Almost Periodic Solutions....Pages 105-119
Stability of Neural Networks....Pages 121-132
The Blood Pressure Distribution....Pages 133-174
Integrate-and-Fire Biological Oscillators....Pages 175-199
Back Matter....Pages 203-216

---

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.
Content:
Front Matter....Pages i-xiii
Introduction....Pages 1-15
Linear and Quasi-Linear Systems with Piecewise Constant Argument....Pages 17-32
The Reduction Principle for Systems with Piecewise Constant Argument....Pages 33-48
The Small Parameter and Differential Equations with Piecewise Constant Argument....Pages 49-69
Stability....Pages 71-88
The State-Dependent Piecewise Constant Argument....Pages 89-104
Almost Periodic Solutions....Pages 105-119
Stability of Neural Networks....Pages 121-132
The Blood Pressure Distribution....Pages 133-174
Integrate-and-Fire Biological Oscillators....Pages 175-199
Back Matter....Pages 203-216
....