{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,25]],"date-time":"2025-10-25T21:53:51Z","timestamp":1761429231552,"version":"3.37.3"},"reference-count":30,"publisher":"World Scientific Pub Co Pte Ltd","issue":"13","funder":[{"name":"the National Key Research and Development Program of China","award":["2016YFB0800601"],"award-info":[{"award-number":["2016YFB0800601"]}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["61472331"],"award-info":[{"award-number":["61472331"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"the Fundamental Research Funds for the Central Universities","award":["XDJK2013C005"],"award-info":[{"award-number":["XDJK2013C005"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2017,12,15]]},"abstract":"<jats:p> In this paper, a novel version of nonlinear model, i.e. a complex-valued love model with two time delays between two individuals in a love affair, has been proposed. A notable feature in this model is that we separate the emotion of one individual into real and imaginary parts to represent the variation and complexity of psychophysiological emotion in romantic relationship instead of just real domain, and make our model much closer to reality. This is because love is a complicated cognitive and social phenomenon, full of complexity, diversity and unpredictability, which refers to the coexistence of different aspects of feelings, states and attitudes ranging from joy and trust to sadness and disgust. By analyzing associated characteristic equation of linearized equations for our model, it is found that the Hopf bifurcation occurs when the sum of time delays passes through a sequence of critical value. Stability of bifurcating cyclic love dynamics is also derived by applying the normal form theory and the center manifold theorem. In addition, it is also shown that, for some appropriate chosen parameters, chaotic behaviors can appear even without time delay. <\/jats:p>","DOI":"10.1142\/s0218127417502005","type":"journal-article","created":{"date-parts":[[2018,1,3]],"date-time":"2018-01-03T03:03:43Z","timestamp":1514948623000},"page":"1750200","source":"Crossref","is-referenced-by-count":7,"title":["Dynamical Behaviors in Complex-Valued Love Model With or Without Time Delays"],"prefix":"10.1142","volume":"27","author":[{"given":"Wei","family":"Deng","sequence":"first","affiliation":[{"name":"Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, P. R. China"},{"name":"Information Technology Center, Southwest University, Chongqing 400715, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4246-3057","authenticated-orcid":false,"given":"Xiaofeng","family":"Liao","sequence":"additional","affiliation":[{"name":"Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, P. R. China"}]},{"given":"Tao","family":"Dong","sequence":"additional","affiliation":[{"name":"Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, P. R. 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