By Ivanka Stamova, Gani Stamov

Using the idea of impulsive differential equations, this publication specializes in mathematical versions which replicate present examine in biology, inhabitants dynamics, neural networks and economics. The authors give you the simple history from the elemental conception and provides a scientific exposition of modern effects with regards to the qualitative research of impulsive mathematical types. inclusive of six chapters, the ebook offers many acceptable suggestions, making them to be had in one resource simply obtainable to researchers attracted to mathematical types and their purposes. Serving as a worthwhile reference, this article is addressed to a large viewers of execs, together with mathematicians, utilized researchers and practitioners.

**Read or Download Applied Impulsive Mathematical Models PDF**

**Best system theory books**

**L2 - Gain and Passivity Techniques in Nonlinear Control**

With appreciate to the 1st version as quantity 218 within the Lecture Notes in Con trol and knowledge Sciences sequence the elemental proposal of the second one variation has remained an identical: to supply a compact presentation of a few easy principles within the classical concept of input-output and closed-loop balance, including a decision of contributions to the new conception of nonlinear powerful and 1foo keep an eye on and passivity-based keep watch over.

**Handbook of Real-World Applications in Modeling and Simulation**

Introduces numerous modeling and simulation equipment and paradigms which are used to give an explanation for and clear up the foremost demanding situations dealing with societyHandbook of Real-World functions in Modeling and Simulation presents a radical rationalization of modeling and simulation within the most precious, present, and main utilized parts of transportation, place of origin protection, drugs, operational learn, army technology, and company modeling.

**The statistical theory of linear systems**

Initially released in 1988, The Statistical conception of Linear platforms offers with identity (in the feel of acquiring a version from info) of multi-input and multi-output linear platforms, particularly platforms in ARMAX and country house shape. The publication emphasizes the underlying conception. It covers constitution thought, specifically attention and parameterization of linear platforms, with targeted emphasis at the research of houses of parameter areas and parameterizations suitable for estimation and version choice; Gaussian greatest chance estimation of the real-valued parameters of linear platforms, with an emphasis on asymptotic concept; version choice, specifically order estimation, through info standards corresponding to AIC or BIC, with an emphasis on asymptotic idea; tactics for calculation of estimates; and approximation through rational features.

- Liapunov Functions and Stability in Control Theory
- Subspace Methods for System Identification (Communications and Control Engineering)
- Synthetic projective geometry
- Stochastic differential equations: an introduction with applications

**Additional info for Applied Impulsive Mathematical Models**

**Sample text**

6 hold. 2. 19 are met. 38 2 Basic Theory 3. 0// for r Ä s Ä 0. 3. 0// for r Ä s Ä 0. 3. Analogous comparison results can be proved for impulsive systems [35, 179] in which minimal solutions are used. 4. Similar results can be proved in terms of functions from the classes V2 and W0 [284, 289, 290]. Next we shall consider a Bihari and Gronwall type integral inequality in a special case with impulses. 22 ([35]). Let the following conditions hold: 1. 1 is met. 2. The functions m W R ! RC ; p W R ! tk 1 ; tk ; tk > t0 .

1. 10 are met. 2. 16) Then: 1. 12). 2. t/ is exponentially stable. Proof. t/j. 18) Now let ! 3. 19), we deduce that S' 2 AP. Let '; 2 AP. 16) it follows that S is a contraction mapping on AP. Then there exists a unique fixed point h 2 D such that Fh D h. t/. t/; 2 PCŒŒ g. C I ; / D . 13). t; /. t/j Ä j je . 16) implies that the unique positive almost periodic solution of Eq. 12) is exponentially stable. 3 A More General n-Dimensional Impulsive Biological Model In this section we shall consider a generalization of the models investigated in Sects.

4 Piecewise Continuous Lyapunov Functions and Lyapunov Functionals 31 impulsive systems restricts the possibilities of Lyapunov’s second method. The fact that the solutions of impulsive systems are piecewise continuous functions requires the introduction of an analogue of the classical Lyapunov functions which have discontinuities of the first kind [34]. By means of such functions it becomes possible to solve basic problems related to the application of Lyapunov’s second method to impulsive systems.