Titlebook: Nonlinear Hybrid Continuous/Discrete-Time Models; Marat Akhmet Book 2011 Atlantis Press 2011 blood pressure distribution.hybrid systems wi

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Almost Periodic Solutions,0.1.2.…, is an identification function, θ. is a strictly ordered sequence of real numbers, unbounded on the left and on the right, ., . = 1.2.…. are fixed integers, and the linear homogeneous system associated with (7.1) satisfies exponential dichotomy. The problem of the existence is studied withou

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The Blood Pressure Distribution, come from a mathematical background and are not familiar with this subject. In Subsection 9.1.2, we build a model as a hybrid system with jumps equation and controlled switching moments and find conditions of oscillations in different types: periodic, almost periodic, . -oscillations with their asy

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Integrate-and-Fire Biological Oscillators,Thus, it was proposed to consider a model of cardiac pacemaker, where signal of fire arises not from an outside stimuli, but in the population of cells itself. Then, the well known conjectures of selfsynchronization were formulated. Solution of these conjectures for identical oscillators [216, 262],

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Linear and Quasi-Linear Systems with Piecewise Constant Argument,In this chapter we start investigation with the most simple linear systems of differential equations with piecewise constant argument. Then the analysis will be extended to quasilinear systems. Existence-uniqueness of solutions, the linear space of solutions, fundamental matrix, stability problems are under discussion.

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The State-Dependent Piecewise Constant Argument,In previous chapters, the differential equations with piecewise constant argument of generalized type (differential equations with piecewise constant arguments) of the form . (6.1) are considered, where . (.) = .. if .. . . < .., . are integers, is an identification function, .. is a strictly increasing sequence of real numbers.

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Stability,y employing the Razumikhin technique [150, 270]. Sufficient conditions are established for stability, uniform stability and uniform asymptotic stability of the trivial solution of such equations. We also provide appropriate examples to illustrate our results.

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Stability of Neural Networks,model of recurrent neural networks (RNNs). The model includes both advanced and delayed arguments. We obtain sufficient conditions for global exponential stability of the equilibrium point. The feasibility of the results are illustrated by examples with numerical simulations.

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Marat AkhmetMost 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 analysi

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