2007, 4(3): 373-402. doi: 10.3934/mbe.2007.4.373

Stochastic and deterministic models for agricultural production networks

1. 

Department of Statistics, University of North Carolina, Hill, NC, United States

2. 

Center for Research in Scientific Computation and Department of Mathematics, North Carolina State University, Raleigh, NC, United States, United States, United States, United States, United States, United States

3. 

National Institute of Statistical Sciences, Research Triangle Park, NC, United States

4. 

Department of Mathematics and Statistics, University of Louisville, KY, United States

5. 

Department of Population Health and Pathobiology, College of Veterinary Medicine, North Carolina State University, Raleigh, NC, United States

Received  February 2007 Revised  March 2007 Published  May 2007

An approach to modeling the impact of disturbances in an agricultural production network is presented. A stochastic model and its approximate deterministic model for averages over sample paths of the stochastic system are developed. Simulations, sensitivity and generalized sensitivity analyses are given. Finally, it is shown how diseases may be introduced into the network and corresponding simulations are discussed.
Citation: P. Bai, H.T. Banks, S. Dediu, A.Y. Govan, M. Last, A.L. Lloyd, H.K. Nguyen, M.S. Olufsen, G. Rempala, B.D. Slenning. Stochastic and deterministic models for agricultural production networks. Mathematical Biosciences & Engineering, 2007, 4 (3) : 373-402. doi: 10.3934/mbe.2007.4.373
[1]

Steady Mushayabasa, Drew Posny, Jin Wang. Modeling the intrinsic dynamics of foot-and-mouth disease. Mathematical Biosciences & Engineering, 2016, 13 (2) : 425-442. doi: 10.3934/mbe.2015010

[2]

H.Thomas Banks, Danielle Robbins, Karyn L. Sutton. Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1301-1333. doi: 10.3934/mbe.2013.10.1301

[3]

Hongxiao Hu, Liguang Xu, Kai Wang. A comparison of deterministic and stochastic predator-prey models with disease in the predator. Discrete & Continuous Dynamical Systems - B, 2019, 24 (6) : 2837-2863. doi: 10.3934/dcdsb.2018289

[4]

Qi Wang, Jingyue Yang, Feng Yu. Boundedness in logistic Keller-Segel models with nonlinear diffusion and sensitivity functions. Discrete & Continuous Dynamical Systems - A, 2017, 37 (9) : 5021-5036. doi: 10.3934/dcds.2017216

[5]

Caglar S. Aksezer. On the sensitivity of desirability functions for multiresponse optimization. Journal of Industrial & Management Optimization, 2008, 4 (4) : 685-696. doi: 10.3934/jimo.2008.4.685

[6]

Uwe Helmke, Michael Schönlein. Minimum sensitivity realizations of networks of linear systems. Numerical Algebra, Control & Optimization, 2016, 6 (3) : 241-262. doi: 10.3934/naco.2016010

[7]

Jaroslaw Smieja, Malgorzata Kardynska, Arkadiusz Jamroz. The meaning of sensitivity functions in signaling pathways analysis. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2697-2707. doi: 10.3934/dcdsb.2014.19.2697

[8]

Alireza Ghaffari Hadigheh, Tamás Terlaky. Generalized support set invariancy sensitivity analysis in linear optimization. Journal of Industrial & Management Optimization, 2006, 2 (1) : 1-18. doi: 10.3934/jimo.2006.2.1

[9]

Behrouz Kheirfam, Kamal mirnia. Comments on ''Generalized support set invariancy sensitivity analysis in linear optimization''. Journal of Industrial & Management Optimization, 2008, 4 (3) : 611-616. doi: 10.3934/jimo.2008.4.611

[10]

Azmy S. Ackleh, Shuhua Hu. Comparison between stochastic and deterministic selection-mutation models. Mathematical Biosciences & Engineering, 2007, 4 (2) : 133-157. doi: 10.3934/mbe.2007.4.133

[11]

Tobias Black. Global generalized solutions to a parabolic-elliptic Keller-Segel system with singular sensitivity. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 119-137. doi: 10.3934/dcdss.2020007

[12]

Xiaoming Yan, Ping Cao, Minghui Zhang, Ke Liu. The optimal production and sales policy for a new product with negative word-of-mouth. Journal of Industrial & Management Optimization, 2011, 7 (1) : 117-137. doi: 10.3934/jimo.2011.7.117

[13]

Marzena Dolbniak, Malgorzata Kardynska, Jaroslaw Smieja. Sensitivity of combined chemo-and antiangiogenic therapy results in different models describing cancer growth. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 145-160. doi: 10.3934/dcdsb.2018009

[14]

Tao Yu. Measurable sensitivity via Furstenberg families. Discrete & Continuous Dynamical Systems - A, 2017, 37 (8) : 4543-4563. doi: 10.3934/dcds.2017194

[15]

Shi Jin, Yingda Li. Local sensitivity analysis and spectral convergence of the stochastic Galerkin method for discrete-velocity Boltzmann equations with multi-scales and random inputs. Kinetic & Related Models, 2019, 12 (5) : 969-993. doi: 10.3934/krm.2019037

[16]

Alejandra Fonseca-Morales, Onésimo Hernández-Lerma. A note on differential games with Pareto-optimal NASH equilibria: Deterministic and stochastic models. Journal of Dynamics & Games, 2017, 4 (3) : 195-203. doi: 10.3934/jdg.2017012

[17]

S.Durga Bhavani, K. Viswanath. A general approach to stability and sensitivity in dynamical systems. Discrete & Continuous Dynamical Systems - A, 1998, 4 (1) : 131-140. doi: 10.3934/dcds.1998.4.131

[18]

Dale McDonald. Sensitivity based trajectory following control damping methods. Numerical Algebra, Control & Optimization, 2013, 3 (1) : 127-143. doi: 10.3934/naco.2013.3.127

[19]

Xiangying Meng, Gemma Huguet, John Rinzel. Type III excitability, slope sensitivity and coincidence detection. Discrete & Continuous Dynamical Systems - A, 2012, 32 (8) : 2729-2757. doi: 10.3934/dcds.2012.32.2729

[20]

Kazimierz Malanowski, Helmut Maurer. Sensitivity analysis for state constrained optimal control problems. Discrete & Continuous Dynamical Systems - A, 1998, 4 (2) : 241-272. doi: 10.3934/dcds.1998.4.241

2018 Impact Factor: 1.313

Metrics

  • PDF downloads (5)
  • HTML views (0)
  • Cited by (0)

[Back to Top]