{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:06:41Z","timestamp":1753888001126,"version":"3.41.2"},"reference-count":27,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,5,30]],"date-time":"2021-05-30T00:00:00Z","timestamp":1622332800000},"content-version":"vor","delay-in-days":149,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100009014","name":"Lanzhou Jiaotong University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100009014","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>In this paper, a discrete\u2010time dynamic duopoly model, with nonlinear demand and cost functions, is established. The properties of existence and local stability of equilibrium points have been verified and analyzed. The stability conditions are also given with the help of the Jury criterion. With changing of the values of parameters, the system shows some new and interesting phenomena in terms to stability and multistability, such as V\u2010shaped stable structures (also called Isoperiodic Stable Structures) and different shape basins of attraction of coexisting attractors. The eye\u2010shaped structures appear where the period\u2010doubling and period\u2010halving bifurcations occur. Finally, by utilizing critical curves, the changes in the topological structure of basin of attraction and the reason of \u201choles\u201d formation are analyzed. As a result, the generation of global bifurcation, such as contact bifurcation or final bifurcation, is usually accompanied by the contact of critical curves and boundary.<\/jats:p>","DOI":"10.1155\/2021\/9978320","type":"journal-article","created":{"date-parts":[[2021,5,30]],"date-time":"2021-05-30T21:50:08Z","timestamp":1622411408000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Stability, Multistability, and Complexity Analysis in a Dynamic Duopoly Game with Exponential Demand Function"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4929-4949","authenticated-orcid":false,"given":"Hui","family":"Li","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4477-3940","authenticated-orcid":false,"given":"Wei","family":"Zhou","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0200-772X","authenticated-orcid":false,"given":"Tong","family":"Chu","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,5,30]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1002\/mma.5826"},{"key":"e_1_2_9_2_2","first-page":"1","article-title":"On the structure and the qualitative behavior of an economic model","volume":"1","author":"El-Metwally H. 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