May  2005, 5(2): 335-352. doi: 10.3934/dcdsb.2005.5.335

Intratrophic predation in a simple food chain with fluctuating nutrient


Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, United States


Department of Mathematics, University of Rhode Island, Kingston, RI 02881, United States


Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409, United States

Received  March 2003 Revised  March 2004 Published  February 2005

A model of interaction between nutrient, prey, and predator with intratrophic predation of the predator and a limiting periodic nutrient input is proposed and studied. Dynamics of the system are shown to depend on two thresholds. These thresholds are expressed in terms of certain periodic solutions of the system. Intratrophic predation can have impact on the model only if both thresholds are greater than zero. In this case positive periodic solutions exist. Numerical techniques are then used to explore the effect of intratrophic predation by examining the mean value and stability of these positive periodic solutions. It is demonstrated numerically that intratrophic predation can increase the stability region of the positive periodic solutions. It can also elevate the mean values of prey population and decrease the mean values of nutrient concentration for stable positive periodic solutions. Moreover, intratrophic predation can eliminate the chaotic behavior of the system when the degree of intratrophic predation is large enough.
Citation: S. R.-J. Jang, J. Baglama, P. Seshaiyer. Intratrophic predation in a simple food chain with fluctuating nutrient. Discrete and Continuous Dynamical Systems - B, 2005, 5 (2) : 335-352. doi: 10.3934/dcdsb.2005.5.335

Keng Deng, Yixiang Wu. Extinction and uniform strong persistence of a size-structured population model. Discrete and Continuous Dynamical Systems - B, 2017, 22 (3) : 831-840. doi: 10.3934/dcdsb.2017041


Johannes Lankeit. Chemotaxis can prevent thresholds on population density. Discrete and Continuous Dynamical Systems - B, 2015, 20 (5) : 1499-1527. doi: 10.3934/dcdsb.2015.20.1499


Marita Thomas. Uniform Poincaré-Sobolev and isoperimetric inequalities for classes of domains. Discrete and Continuous Dynamical Systems, 2015, 35 (6) : 2741-2761. doi: 10.3934/dcds.2015.35.2741


Henri Berestycki, Jean-Pierre Nadal, Nancy Rodíguez. A model of riots dynamics: Shocks, diffusion and thresholds. Networks and Heterogeneous Media, 2015, 10 (3) : 443-475. doi: 10.3934/nhm.2015.10.443


Donald L. DeAngelis, Bo Zhang. Effects of dispersal in a non-uniform environment on population dynamics and competition: A patch model approach. Discrete and Continuous Dynamical Systems - B, 2014, 19 (10) : 3087-3104. doi: 10.3934/dcdsb.2014.19.3087


Maria Paola Cassinari, Maria Groppi, Claudio Tebaldi. Effects of predation efficiencies on the dynamics of a tritrophic food chain. Mathematical Biosciences & Engineering, 2007, 4 (3) : 431-456. doi: 10.3934/mbe.2007.4.431


Jean-Jacques Kengwoung-Keumo. Dynamics of two phytoplankton populations under predation. Mathematical Biosciences & Engineering, 2014, 11 (6) : 1319-1336. doi: 10.3934/mbe.2014.11.1319


Paul L. Salceanu. Robust uniform persistence in discrete and continuous dynamical systems using Lyapunov exponents. Mathematical Biosciences & Engineering, 2011, 8 (3) : 807-825. doi: 10.3934/mbe.2011.8.807


Kaifa Wang, Aijun Fan. Uniform persistence and periodic solution of chemostat-type model with antibiotic. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 789-795. doi: 10.3934/dcdsb.2004.4.789


Paul L. Salceanu. Robust uniform persistence for structured models of delay differential equations. Discrete and Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021258


Hua Nie, Sze-Bi Hsu, Feng-Bin Wang. Global dynamics of a reaction-diffusion system with intraguild predation and internal storage. Discrete and Continuous Dynamical Systems - B, 2020, 25 (3) : 877-901. doi: 10.3934/dcdsb.2019194


Evariste Sanchez-Palencia, Philippe Lherminier. Paradoxes of vulnerability to predation in biological dynamics and mediate versus immediate causality. Discrete and Continuous Dynamical Systems - S, 2020, 13 (8) : 2195-2209. doi: 10.3934/dcdss.2020185


Alex John Quijano, Michele L. Joyner, Edith Seier, Nathaniel Hancock, Michael Largent, Thomas C. Jones. An aggregate stochastic model incorporating individual dynamics for predation movements of anelosimus studiosus. Mathematical Biosciences & Engineering, 2015, 12 (3) : 585-607. doi: 10.3934/mbe.2015.12.585


Eric Ruggieri, Sebastian J. Schreiber. The Dynamics of the Schoener-Polis-Holt model of Intra-Guild Predation. Mathematical Biosciences & Engineering, 2005, 2 (2) : 279-288. doi: 10.3934/mbe.2005.2.279


Hal L. Smith, Horst R. Thieme. Persistence and global stability for a class of discrete time structured population models. Discrete and Continuous Dynamical Systems, 2013, 33 (10) : 4627-4646. doi: 10.3934/dcds.2013.33.4627


Andrea Caravaggio, Luca Gori, Mauro Sodini. Population dynamics and economic development. Discrete and Continuous Dynamical Systems - B, 2021, 26 (11) : 5827-5848. doi: 10.3934/dcdsb.2021178


Steven M. Pederson. Non-turning Poincaré map and homoclinic tangencies in interval maps with non-constant topological entropy. Conference Publications, 2001, 2001 (Special) : 295-302. doi: 10.3934/proc.2001.2001.295


Anatoli F. Ivanov. On global dynamics in a multi-dimensional discrete map. Conference Publications, 2015, 2015 (special) : 652-659. doi: 10.3934/proc.2015.0652


Yongki Lee, Hailiang Liu. Thresholds for shock formation in traffic flow models with Arrhenius look-ahead dynamics. Discrete and Continuous Dynamical Systems, 2015, 35 (1) : 323-339. doi: 10.3934/dcds.2015.35.323


Wei Feng, Xin Lu, Richard John Donovan Jr.. Population dynamics in a model for territory acquisition. Conference Publications, 2001, 2001 (Special) : 156-165. doi: 10.3934/proc.2001.2001.156

2020 Impact Factor: 1.327


  • PDF downloads (44)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]