{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T21:47:58Z","timestamp":1649022478047},"reference-count":22,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2006,5]]},"abstract":" In this paper we study the existence, uniqueness and stability of periodic solutions for a two-neuron network system with or without external inputs. The system consists of two identical neurons, each possessing nonlinear feedback and connected to the other neuron via a nonlinear sigmoidal activation function. In the absence of external inputs but with appropriate conditions on the feedback and connection strengths, we prove the existence, uniqueness and stability of periodic solutions by using the Poincar\u00e9\u2013Bendixson theorem together with Dulac's criterion. On the other hand, for the system with periodic external inputs, combining the techniques of the Liapunov function with the contraction mapping theorem, we propose some sufficient conditions for establishing the existence, uniqueness and exponential stability of the periodic solutions. Some numerical results are also provided to demonstrate the theoretical analysis. <\/jats:p>","DOI":"10.1142\/s0218127406015386","type":"journal-article","created":{"date-parts":[[2006,8,21]],"date-time":"2006-08-21T11:10:02Z","timestamp":1156158602000},"page":"1405-1417","source":"Crossref","is-referenced-by-count":1,"title":["ON PERIODIC SOLUTIONS OF A TWO-NEURON NETWORK SYSTEM WITH SIGMOIDAL ACTIVATION FUNCTIONS"],"prefix":"10.1142","volume":"16","author":[{"given":"CHENG-HSIUNG","family":"HSU","sequence":"first","affiliation":[{"name":"Department of Mathematics, National Central University, Chung-Li 32001, Taiwan, ROC"}]},{"given":"SUH-YUH","family":"YANG","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National Central University, Chung-Li 32001, Taiwan, ROC"}]},{"given":"TING-HUI","family":"YANG","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Tamkang University, Tamsui, Taipei County 25137, Taiwan, ROC"}]},{"given":"TZI-SHENG","family":"YANG","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Tunghai University, Taichung 40704, Taiwan, ROC"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139994274526"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.2000.6890"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1142\/9789812798589"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1109\/31.7600"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1109\/31.7601"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1002\/cta.4490210505"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(95)00203-0"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4426-4"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.81.10.3088"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1109\/81.841852"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1142\/S021812749900064X"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1142\/S021812740401134X"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.39.347"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(91)90236-3"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/0893-6080(92)90011-7"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(96)00215-1"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-0392-3"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139998344015"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127401002055"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(92)90038-K"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.50.4206"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1109\/31.81867"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127406015386","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:09:56Z","timestamp":1565136596000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127406015386"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,5]]},"references-count":22,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2006,5]]}},"alternative-id":["10.1142\/S0218127406015386"],"URL":"https:\/\/doi.org\/10.1142\/s0218127406015386","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,5]]}}}