Time effect on the dynamical behavior of a life energy system dynamic model
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Authors
Changjin Xu
- Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550004, P. R. China.
Peiluan Li
- School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, P. R. China.
Abstract
This article is concerned with a life energy system dynamic model with two different delays. A set of sufficient criteria
which ensures the local stability and the existence of Hopf bifurcation for the model is derived. Some explicit formulas which
determine the nature of Hopf bifurcations are obtained by means of the normal form theory and center manifold theorem. Our
analytical findings are supported by numerical experiments. Finally, a brief conclusion is included.
Share and Cite
ISRP Style
Changjin Xu, Peiluan Li, Time effect on the dynamical behavior of a life energy system dynamic model, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 2, 656--670
AMA Style
Xu Changjin, Li Peiluan, Time effect on the dynamical behavior of a life energy system dynamic model. J. Nonlinear Sci. Appl. (2017); 10(2):656--670
Chicago/Turabian Style
Xu, Changjin, Li, Peiluan. "Time effect on the dynamical behavior of a life energy system dynamic model." Journal of Nonlinear Sciences and Applications, 10, no. 2 (2017): 656--670
Keywords
- Life energy system model (LESM)
- delay
- stability
- Hopf bifurcation.
MSC
References
-
[1]
J.-D. Cao, M. Xiao, Stability and Hopf bifurcation in a simplified BAM neural network with two time delays, IEEE Trans. Neural Netw., 18 (2007), 416–430.
-
[2]
Z.-S. Cheng, J.-D. Cao, Hybrid control of Hopf bifurcation in complex networks with delays, Neurocomputing, 131 (2014), 164–170.
-
[3]
J. Hale, Theory of functional differential equations, Second edition. Applied Mathematical Sciences, Springer-Verlag, New York-Heidelberg (1977)
-
[4]
B. D. Hassard, N. D. Kazarinoff, Y.-H. Wan, Theory and applications of Hopf bifurcation, London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge-New York (1981)
-
[5]
J.-Q. Hu, J.-D. Cao, T. Hayat, Stability and Hopf bifurcation analysis for an energy resource system, Nonlinear Dynam., 78 (2014), 219–234.
-
[6]
X. Huang, How do simple energy activities comprise complex behavior of life systems?: A conceptual synthesis and decomposition of the energy structure of life systems, Ecol. Model., 165 (2003), 79–89.
-
[7]
X. Huang, On the energy trait control phenomena in ecosystems, Ecol. Model., 211 (2008), 36–46.
-
[8]
X. Huang, Y.-G. Zu, The LES population model: essentials and relationship to the Lotka-Volterra model, Ecol. Model., 143 (2001), 215–225.
-
[9]
S. E. Jøgensen, Use of models as experimental tool to show that structural changes are accompanied by increased energy, Ecol. Model., 41 (1988), 117–126.
-
[10]
S. A. L. M. Kooijman, Dynamic energy and mass budgets in biological systems, Cambridge Univ. Press, Cambridge (2000)
-
[11]
S. A. L. M. Kooijman, T. Andersen, B. W. Kooi, Dynamic energy budget representations of stoichiometric constraints on population dynamics, Ecol., 85 (2004), 1230–1243.
-
[12]
S. A. L. M. Kooijman, B. W. Kooi, T. G. Hallam, The application of mass and energy conservation laws in physiologically structured population models of heterotrophic organisms, J. Theor. Biol., 197 (1999), 371–392.
-
[13]
S. A. L. M. Kooijman, T. A. Troost, Quantitative steps in the evolution of metabolic organisation as specified by the dynamic energy budget theory, Biol. Rev., 82 (2007), 113–142.
-
[14]
Y. Kuang, Delay differential equations with applications in population dynamics, Mathematics in Science and Engineering, Academic Press, Inc., Boston, MA (1993)
-
[15]
M.-X. Liao, C.-J. Xu, X.-H. Tang, Stability and Hopf bifurcation for a competition and cooperation model of two enterprises with delay, Commun. Nonlinear Sci. Numer. Simul., 19 (2014), 3845–3856.
-
[16]
X.-H. Lin, H. Wang, Stability analysis of delay differential equations with two discrete delays, Can. Appl. Math. Q., 20 (2012), 519–533.
-
[17]
R. L. Lindeman , Seasonal food-cycle dynamics in a senescent lake, Am. Midl. Nat., 26 (1941), 636–673.
-
[18]
R. L. Lindeman, The trophicdynamic aspect of ecology , Ecol., 23 (1942), 399–417.
-
[19]
E. B. Muller, S. A. L. M. Kooijman, P. J. Edmunds, F. J. Doyle, R. M. Nisbe, Dynamic energy budgets in syntrophic symbiotic relationships between heterotrophic hosts and photoautotrophic symbionts, J. Theor. Biol., 259 (2009), 44–57.
-
[20]
H .T. Odum, Systems ecology, John Wiley & Sons, New York, NY (1983)
-
[21]
S.-G. Ruan, J.-J. Wei, On the zeros of transcendental functions with applications to stability of delay differential equations with two delays, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 10 (2003), 863–874.
-
[22]
M. Xiao, J.-D. Cao, W.-X. Zheng, Bifurcation with regard to combined interaction parameter in a life energy system dynamic model of two components with multiple delays, J. Franklin Inst., 348 (2011), 2647–2669.
-
[23]
W.-Y. Xu, J.-D. Cao, M. Xiao, Bifurcation analysis and control in exponential RED algorithm, Neurocomputing, 129 (2014), 232–245.
-
[24]
W.-Y. Xu, J.-D. Cao, M. Xiao, Bifurcation analysis of a class of (n + 1)-dimension internet congestion control systems, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 25 (2015), 17 pages.
-
[25]
W.-Y. Xu, T. Hayat, J.-D. Cao, M. Xiao, Hopf bifurcation control for a fluid flow model of internet congestion control systems via state feedback, IMA J. Math. Control Inform., 33 (2016), 69–93.
-
[26]
C.-J. Xu, Y.-S. Wu, Bifurcation and control of chaos in a chemical system, Appl. Math. Model., 39 (2015), 2295–2310.
-
[27]
C.-R. Zhang, Y.-G. Zu, B.-D. Zheng, Stability analysis in a two-dimensional life energy system model with delay, Ecol. Model., 193 (2006), 691–702.