By Ivanka Stamova, Gani Stamov

Using the idea of impulsive differential equations, this booklet makes a speciality of mathematical versions which mirror present learn in biology, inhabitants dynamics, neural networks and economics. The authors give you the uncomplicated historical past from the basic concept and provides a scientific exposition of contemporary effects on the topic of the qualitative research of impulsive mathematical versions. along with six chapters, the ebook offers many acceptable ideas, making them to be had in one resource simply available to researchers drawn to mathematical types and their functions. Serving as a priceless reference, this article is addressed to a large viewers of pros, together with mathematicians, utilized researchers and practitioners.

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

**Similar system theory books**

**Analysis and Control of Boolean Networks: A Semi-tensor Product Approach **

Research and regulate of Boolean Networks offers a scientific new method of the research of Boolean keep an eye on networks. the basic device during this technique is a unique matrix product referred to as the semi-tensor product (STP). utilizing the STP, a logical functionality could be expressed as a traditional discrete-time linear approach.

This e-book comprises the lawsuits of the Workshop on Networked Embedded Sensing and keep watch over. This workshop goals at bringing jointly researchers engaged on diverse features of networked embedded platforms on the way to trade examine reports and to spot the most medical demanding situations during this intriguing new sector.

**Quantitative Conservation Biology**

Conservation biology is predicated not just at the normal suggestions, yet at the particular equipment, of inhabitants ecology to either comprehend and are expecting the viability of infrequent and endangered species and to figure out how most sensible to regulate those populations. the necessity to behavior quantitative analyses of viability and administration has spawned the sector of "population viability analysis," or PVA, which, in flip, has pushed a lot of the hot improvement of worthwhile and sensible inhabitants research and modeling in ecology regularly.

**Sliding Mode Control: The Delta-Sigma Modulation Approach**

This monograph provides a unique approach to sliding mode keep an eye on for switch-regulated nonlinear platforms. The Delta Sigma modulation method permits one to enforce a continual keep watch over scheme utilizing one or a number of, self reliant switches, therefore successfully merging the to be had linear and nonlinear controller layout strategies with sliding mode keep an eye on.

- Mathematical Ecology of Populations and Ecosystems
- Lectures on the theory of elliptic functions. Analysis
- Robust Design: A Repertoire of Biological, Ecological, and Engineering Case Studies (Santa Fe Institute Studies on the Sciences of Complexity)
- Adaptive Control Design and Analysis
- Robust control design: an optimal control approach
- Self-organized biological dynamics & nonlinear control

**Additional info for Applied Impulsive Mathematical Models**

**Example text**

T/. 2. The sequence f˛k g is almost periodic and 1 < ˛k Ä 0; k D ˙1; ˙2; : : :. 3. ftk g 2 UAPS. s/ exp ) ˛. /d s for tk 1 < s Ä t Ä tk ; k D ˙1; ˙2; : : :. 6) in Chap. 3) the matrix 8 n Z t ˆ ˆ exp ˛. 1 C ˛i / exp ˆ ˆ ˆ : iDm tm 1 < s Ä tm < t k o ; tk Z t 1 < s Ä t Ä tk ; ) ˛. 4. 5. 6. The sequence f k g; k D ˙1; ˙2; : : :, is almost periodic. 7 in [284]. 1. 6 hold. t/j < "; t 2 R; j˛kCq ˛k j < "; q 2 P; k D ˙1; ˙2; : : : I j kCq k j < "; q 2 P; k D ˙1; ˙2; : : : I q jtk rj < "1 ; q 2 P; r 2 T; k D ˙1; ˙2; : : :.

0/ has a dominant role. 23) holds. 23) is called the Razumikhin condition, and the corresponding technique is known as the Razumikhin technique. 17). 20. A function W W R ! RC belongs to the class W0 if: 1. t; 0/ D 0; t 2 R. 2. t; x/ is locally Lipschitz continuous with respect to its second argument. 3. tks ; x/ holds. Let the function W 2 W0 and x 2 PCŒR; . t// : In the investigation of the qualitative properties of solutions of differential equations, it is well known that employing several Lyapunov functions is more useful than employing a single one since each function can satisfy less rigid requirements.

Let the following conditions hold. 1. 6 hold for k D 1; 2; : : :. 2. 18 are met. 3. The function V W Œt0 ; 1/ ! 0// for r Ä s Ä 0. 20. 21. Let the following conditions hold. 1. 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.