DYNAMICS OF NONLINEAR TIME DELAY SYSTEMS PDF

and Weihua Li2 1School of Electrical, Computer and Telecommunications Engineering 2School of Mechanical, Materials and Mechatronics Engineering University of Wollongong, Wollongong, NSW 2522 Australia 1. Introduction Time delays are often encountered by practical control[r]

of the sequence corresponds to a choice of an integerr that defines the discretization of the delay in r in-tervals of same length. For growing discretizations theproblems are shown to have conservatism reductionproperties. The building of sequences of[r]

of Shandong (Y2007G06) and the Doctoral Foundation of Qingdao University of Science and Technology. 7. References Lewis,F.L.; Yesildirek A. & Liu K.(1996). Multilayer neural-net robot controller with guaranteed tracking performance. IEEE Trans.on Neural Networks, Vol.[r]

6. Conclusion
The love triangle is affected by human personalities and exter- nal stimulations, which leads to a chaotic relationship or maybe a quiet one. This effect in the integer-order model of a love triangle was discussed with three different nonlinearities. Maximum Lyapunov exponent[r]

x; otherwise it is called nonoscillatory. Finally,(NE) is called oscillatory if all its solutions are oscillatory.In recent years, there has been a great deal of work on the oscillatory behavior of so-lutions of some second-order dynamic equations. To the best of our know[r]

˘ılenko and N. A. Perestyuk, Impulsive Differential Equations, vol. 14 of World Scientific Serieson Nonlinear Science. Series A: Monographs and Treatises, World Scientific, River Edge, NJ, USA, 1995.13 S. Wu and X. Meng, “Boundedness of nonlinear differential systems[r]

has wide basins of attractions (Wuensche [35]), that is, lowsensitivity to initial conditions. This property is considereddesirable for any formal scheme in models of living systems.In this work, the S-system has been selected to representnonlinear interactions within genetic re[r]

dx(t)dt= Ax(t) + µf(t, x(t + θ)), t ≥ 0, −h  θ  0, (1)where x(.) ∈ E, A ∈ L(E), E is a Banach space, the operator f : R+× E −→ E is continuous in tand satisfies all following conditions:f(t, 0) = 0, (2)f(t, y(t + θ)) − f(t, z(t + θ))  L sup−hθ0y(t + θ) − z(t + θ). (3)In [1], K.G.Valeev prov[r]

=u,(3.43)and soTu≤u. For this case, if we letΩ2=x ∈ Ꮾ |x <H4, (3.44)thenTu≤u,foru ∈ ᏼ ∩ ∂Ω2. (3.45)In either cases, application of part (ii) of Theorem 2.1 yields a fixed point u of T be-longing to ᏼ∩ (Ω2\ Ω1), which in turn yields a pair (u,v) satisfying (1.[r]

=u,(3.43)and soTu≤u. For this case, if we letΩ2=x ∈ Ꮾ |x <H4, (3.44)thenTu≤u,foru ∈ ᏼ ∩ ∂Ω2. (3.45)In either cases, application of part (ii) of Theorem 2.1 yields a fixed point u of T be-longing to ᏼ∩ (Ω2\ Ω1), which in turn yields a pair (u,v) satisfying (1.[r]

Formula"* http://www.mathworks.com/access/helpdesk/help/techdoc/index.html?/access/helpdesk/help/techdoc/ref/ode23.html.! Shampine, L. F. and M. W. Reichelt, "The MATLAB ODE Suite," SIAM Journal on Scientific Computing, Vol. 18, 1997, pp 1-22.!•  Adams-Bashforth-Moulton Algorithm"•  Modified Rosenbroc[r]

[3, 13] for other classes of nonlinearities.AcknowledgmentsThe author is very grateful for the financial support and the facilities provided by KingFahd University of Petroleum and Minerals. Thanks are due also to the anonymous ref-erees.12 An impulsive Gronwall-Bihari type inequalityRe[r]

Hindawi Publishing CorporationFixed Point Theory and ApplicationsVolume 2011, Article ID 867932, 19 pagesdoi:10.1155/2011/867932Research ArticleAbout Robust Stability of Caputo LinearFractional Dynamic Systems with Time Delaysthrough Fixed Point TheoryM. De la SenFaculty of