{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,1,23]],"date-time":"2023-01-23T21:18:06Z","timestamp":1674508686205},"reference-count":21,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2009,3]]},"abstract":"<jats:p> The original Bass product growth model has been modified in this paper by incorporating a diffusion term and a delay. The imitation parameter \u03b2 is assumed to be negative which represents the effect of \"negative-word-of-mouth\" (NWOM). The occurrence of Hopf bifurcation at the positive equilibrium of the remaining market growth u* was proved as \u03b2 passes through a critical value. The analysis of the distribution of eigenvalues led to the following conclusion. The unstable positive equilibrium state at zero diffusion (d = 0) under NWOM becomes stable when d &gt; 0 for a wide range of \u03b2. This observation suggests that when there is a critical NWOM, favorable conditions for the future stable state of u* could be achieved by promoting the product in space (new geographical areas). <\/jats:p>","DOI":"10.1142\/s0218127409023482","type":"journal-article","created":{"date-parts":[[2009,5,28]],"date-time":"2009-05-28T06:49:43Z","timestamp":1243493383000},"page":"1059-1067","source":"Crossref","is-referenced-by-count":7,"title":["HOPF BIFURCATION ANALYSIS OF DIFFUSIVE BASS MODEL WITH DELAY UNDER \"NEGATIVE-WORD-OF-MOUTH\""],"prefix":"10.1142","volume":"19","author":[{"given":"A. W.","family":"WIJERATNE","sequence":"first","affiliation":[{"name":"Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. 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