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Most general differential equations with piece-wise constant argument are investigated
New technique of analysis is used. A new model of blood pressure distribution is introduced with complete analysis Synchronization of quite identical integrate-and-fire oscillators is proved
General model of quite identical integrate-and-fire oscillators is constructed
Model of recurrent neural networks with continuous/discrete-time is investigated
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 Level »Upper undergraduate
Keywords »blood pressure distribution - hybrid systems with continuous/discrete-time - integrate-and-fire biological oscillators - neural networks - piecewise constant argument