Cisco Webex, Online seminar
(線上演講 Cisco Webex)
Delay-Induced Stability Classification in Some Population Models
Bapan Ghosh (Indian Institute of Technology Indore)
Abstract:
Before the start of the main presentation, I will briefly showcase the small subtopics covered by our research group. The talk mainly focuses on delay differential equations and stability analysis. Time delays are often essential in modeling various physical, biological, chemical, and economic processes due to non-instantaneous feedback. In population dynamics, delays such as gestation delay, maturation delay, and dispersal delay are incorporated into models to capture more realistic features. We first define several delay-induced stability classifications of equilibria, namely:
(i) saddle invariance,
(ii) stability invariance,
(iii) stability change,
(iv) stability switching,
(v) instability invariance, and
(vi) instability switching.
Our primary objective is to examine whether all the above stability scenarios can occur in a single population model with a single discrete time delay. Furthermore, we investigate whether any of these scenarios can arise through multiple mechanisms. The stability of equilibria is determined by the crossing of eigenvalues through the imaginary axis, from the left half of the complex plane to the right half and vice-versa. The variation of the leading real part of the eigenvalues and the delay-induced bifurcation diagram are demonstrated numerically. Our minimal model, consisting of two species with a single time-delay parameter, exhibits all six stability classifications. In addition, we identify a degenerate case in which the equilibrium remains stable for all delays, possibly except at a critical delay.
Finally, we discuss the limitations of this study in the context of real ecosystems. Nevertheless, this investigation is useful for understanding the stability analysis of delay differential equations in general. At the end of the talk, I will briefly introduce my institute and opportunities offered here for international collaboration for researchers and faculty members of Taiwan.
Meeting number (access code): 2516 722 1102
Meeting password: 6pbP4v3aw3s (67274832 when dialing from a phone or video system)
Organizers: Feng-Bin Wang (Chang Gung U.), Chang-Hong Wu (NYCU) & Chang-Yuan Cheng (NKNU)
