{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,27]],"date-time":"2024-07-27T21:55:18Z","timestamp":1722117318825},"reference-count":32,"publisher":"World Scientific Pub Co Pte Lt","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2012,11]]},"abstract":"<jats:p> The fundamental local passivity theory asserts that a wide spectrum of complex behaviors may exist if the cells in the reaction\u2013diffusion are not locally passive. This local passivity principle has provided a powerful tool for studying the complexity in a homogeneous lattice formed by coupled cells. In this paper, the complexity matrix Y<jats:sub>Q<\/jats:sub>(s), which is the tool for testing the local passivity theory, is modified based on the characteristic polynomial A<jats:sub>Q<\/jats:sub>(\u03bb). Then, the local passivity theory is applied to the study of the Oregonator CNN to judge if the cell parameters of a CNN are chosen at the edge of chaos. Analysis of the bifurcation and the numerical simulations show that nonzero diffusion term in Oregonator CNN may cause a reaction\u2013diffusion equation oscillating under the appropriate choice of diffusion coefficient if the local passivity theory is not satisfied. That is, if the cell parameters of a CNN are chosen at the edge of chaos, the system is potentially unstable. <\/jats:p>","DOI":"10.1142\/s0218127412502859","type":"journal-article","created":{"date-parts":[[2012,12,13]],"date-time":"2012-12-13T04:14:17Z","timestamp":1355372057000},"page":"1250285","source":"Crossref","is-referenced-by-count":1,"title":["EXTENDING LOCAL PASSIVITY THEORY AND HOPF BIFURCATION AT THE EDGE OF CHAOS IN OREGONATOR CNN"],"prefix":"10.1142","volume":"22","author":[{"given":"CHANGBING","family":"TANG","sequence":"first","affiliation":[{"name":"Adaptive Networks and Control Lab, Electronic Engineering Department, Fudan University, Shanghai 200433, P. R. China"}]},{"given":"FANGYUE","family":"CHEN","sequence":"additional","affiliation":[{"name":"School of Science, Hangzhou Dianzi University, Hangzhou, Zhejiang, Hangzhou 310018, P. R. China"}]},{"given":"JIANBO","family":"WANG","sequence":"additional","affiliation":[{"name":"Adaptive Networks and Control Lab, Electronic Engineering Department, Fudan University, Shanghai 200433, P. R. China"}]},{"given":"XIANG","family":"LI","sequence":"additional","affiliation":[{"name":"Adaptive Networks and Control Lab, Electronic Engineering Department, Fudan University, Shanghai 200433, P. R. 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