American Institute of Mathematical Sciences

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

Intratrophic predation in a simple food chain with fluctuating nutrient

S. R.-J. Jang 1, , J. Baglama 2, and  P. Seshaiyer 3,

1. 

Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, United States
2. 

Department of Mathematics, University of Rhode Island, Kingston, RI 02881, United States
3. 

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.
Keywords: uniform persistence., thresholds, Poincaré map, intratrophic predation, Population dynamics.
Mathematics Subject Classification: 92D2.
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
[1]

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
[2]

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
[3]

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
[4]

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
[5]

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
[6]

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
[7]

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
[8]

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
[9]

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
[10]

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
[11]

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
[12]

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
[13]

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
[14]

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
[15]

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
[16]

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
[17]

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
[18]

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
[19]

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
[20]

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

Tools

Metrics

  • PDF downloads (41)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy