时滞脉冲细胞神经网络的定性研究

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1、Æ“Ò10530ÆÒ201510111137©aÒO175.12—?a¬ÆØ©ž¢óÀ[œ²ä½5ïÄÆž

2、mpulsesanddelaysCandidateChaonanMaoSupervisorandRankProf.JiqinDengCollegeMathematicsandComputationalScienceProgramMathematicsSpecializationFunctionTheoryanditsApplicationDegreeMasterofScienceUniversityXiangtanUniversityDateApril10th,2018Á‡©Ì‡ïÄ´ž¢óÀ²䕧§$^

3、ØÄ:½né±e˜a•§±Ï)!)Ú)•½5?1?Ø"8Pn>>0>>xi(t)=ai(t)xi(t)+[bij(t)fj(xj(t))>>j=1><+dij(t)gj(xj(tij(t)))]+ui(t);t6=tk;t0;>>+>>>>
xi(tk)=xi(tk)xi(tk)=cikxi(tk);t=tk;>:xi(t)='i(t);k=1;2;:::;i=1;2;:::;n;t2[;0]:•:•)ʇܩµ1˜Ü©§ïĵÚyG¶1Ü©§ïÄ‘óÀDCNNs±Ï)•3Ú•˜5¶1

4、nÜ©§ïÄ‘óÀDCNNs)•3Ú•˜5¶1oÜ©§ïÄ‘óÀDCNNs)•ê•½5¶•,ÏLü‡~f5ü«(J"'…c:DCNNs¶±Ï)¶•3•˜5¶•ê•½5"AbstractInthepaper,Byusingthexedpointtheorem,weconsiderthefollowingcellularneuralnetworkswithimpulsesanddelays.8Pn>>0>>xi(t)=ai(t)xi(t)+[bij(t)fj(xj(t))>>j=1><+dij(t)gj

5、(xj(tij(t)))]+ui(t);t6=tk;t0;>>+>>>>
xi(tk)=xi(tk)xi(tk)=cikxi(tk);t=tk;>:xi(t)='i(t);k=1;2;:::;i=1;2;:::;n;t2[;0]:Thisiscomposedofvechapters:InChapter1,weintroducethedevelopmentandresearchofthecellularneuralnetworkandourmainworks;InChapter2,westudyth

6、eexistenceanduniquenessofperiodicsolutionsoftheaboveDCNNswithimpulses;InChapter3,westudytheexistenceanduniquenessofgeneralsolutionsoftheaboveDCNNswithimpulses;InChapter4,westudyexponentialstabilityofgeneralsolutionsoftheaboveDCNNswithimpulses;InChapter5,wegiv

7、etwoexamplestoillustrateourresults.Keyword:Cellularneuralnetworkswithimpulsesanddelays;Periodicsolu-tion;Existenceanduniqueness;Exponentialstability.8¹1˜ÙXØ...............................................................1x1.1ïĵ†yG............................

8、..........................1x1.2©(.............................................................11Ù±Ï)•3!•˜5ïÄ.....................................2x2.1ý•£.............................