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Dynamic Problems Researches of Several Types of Impulsive Dynamic Systems

Author: WangXiaoMei
Tutor: ZhongShouMing
School: University of Electronic Science and Technology
Course: Applied Mathematics
Keywords: impulsive dynamic system permanence semi-trivial periodic solution Lyapunov function locally asymptotically stability globally exponential stability positive periodic solution
CLC: O19
Type: PhD thesis
Year: 2011
Downloads: 97
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Abstract


In many continuous gradation processes either the system, as a result of somekinds of reason, the mode of some systems may be suffered by the sudden change or thedisturbance in a short time, thus the original path is changed, this kind of phenomenonis called the impulse phenomenon, the impulsive differential dynamic system canprovide the good description to the sudden change variation process under theinstantaneous disturbance in terms of the mathematical treatment, these systems withimpulses have some mixed natures, both continuous and discrete. Therefore the researchof impulsive differential systems is more realistic than the corresponding research ofcontinual differential systems.In this paper, three kinds of dynamic questions with the impulsive dynamicsystems are studied, they are biology dynamic systems with impulses, bidirectionalassociative memory (BAM) neural network with impulses , neutral system withimpulses, and carried discusses thoroughly on some related question of hot spot domain,obtained quite perfect and important result.Firstly, population dynamical behaviors of the impulse control ecological system arestudied numerically and analytically. On the basis of the biological theories andsignificance, three kinds of ecological systems with impulsive control strategy areestablished. By using the theories of impulsive equation, we obtain critical conditionwhich can guarantees the global asymptotical stability of the semi-trivial periodicsolution and persistence of all species. In order to show the correctness and feasibility ofmathematical theoretical works, long-term dynamical behaviors of the system arestudied with emulated data. These results show that the impulsive control strategy has aprofound effect on the population dynamical behavior of three ecological systems,hence, it is interesting to point out that the key factors for long-term persistence isimpulsive control strategy.Secondly, dynamical questions of the BAM neural network systems with impulsescontrol ecological are studied ,three kinds of BAM systems with impulsive control strategy are established, On the basis of the inequality theory, contraction mappingtheory and Lyapunov stability theory, some new sufficient conditions are established forthe existence and uniqueness and globally exponential stability of equilibrium of theconstant coefficient BAM system, then existence and globally exponential stability ofperiodic solution problem of the variable coefficient BAM system with distributed andmixed time delay is studied, which generalized and improved the previously knownresults, these conclusions have certain value to the later research.Finally, population dynamical question of the neutral system with impulse controlecological is studied, a neutral system with impulsive control strategy is established ,onthe basis of some analysis techniques and the theory of coincidence degree, somesufficient conditions for the existence of positive periodic solution of the neutralprey-predator system with impulsive and delay are obtained. It should be stressed thatthe neutral impulsive delay system possesses the original periodicity of the neutral noimpulsive system using the appropriate linear periodic impulsive perturbations. Theforegoing results have the potential to be useful for the study of the neutral systems withimpulses and delays.

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CLC: > Mathematical sciences and chemical > Mathematics > Dynamical systems theory
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