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Your search keyword '"*DELAY differential equations"' showing total 2 results
2 results on '"*DELAY differential equations"'

1. Oscillatory behavior in microbial continuous culture with discrete time delay

Author

Lian, Hansheng, Feng, Enmin, Li, Xiaofang, Ye, Jianxiong, and Xiu, Zhilong

Subjects
*TIME delay systems, *MATHEMATICAL models, *ORGANIC compounds, *FERMENTATION, *DELAY differential equations, *NUMERICAL analysis, *SIMULATION methods & models, *PHASE diagrams
Abstract

Abstract: By introducing discrete time delay into the model for producing 1,3-propanediol by microbial continuous fermentation, we consider the stability and Hopf bifurcation of the delay differential system. Through numerical simulations, we get the rule of branch value changing with parameter and draw the pictures of periodic solutions and phase diagrams with specified parameters. The effect of time delay suggests that the system can qualitatively describe oscillatory phenomena occurring in the experiment. [Copyright &y& Elsevier]

Published
2009
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2. Complex dynamics in a prey predator system with multiple delays

Author

Gakkhar, Sunita and Singh, Anuraj

Subjects
*DELAY differential equations, *PREDATION, *NONLINEAR differential equations, *FUNCTIONAL analysis, *EXISTENCE theorems, *BIFURCATION theory, *HOPF algebras, *NUMERICAL analysis, *SIMULATION methods & models
Abstract

Abstract: The complex dynamics is explored in a prey predator system with multiple delays. Holling type-II functional response is assumed for prey dynamics. The predator dynamics is governed by modified Leslie–Gower scheme. The existence of periodic solutions via Hopf-bifurcation with respect to both delays are established. An algorithm is developed for drawing two-parametric bifurcation diagram with respect to two delays. The domain of stability with respect to τ 1 and τ 2 is thus obtained. The complex dynamical behavior of the system outside the domain of stability is evident from the exhaustive numerical simulation. Direction and stability of periodic solutions are also determined using normal form theory and center manifold argument. [Copyright &y& Elsevier]

Published
2012
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