Monitoring of ecological systems is one of the major
issues in ecosystem research. The concepts and methodology of
mathematical systems theory provide useful tools to face this
problem. In many cases, state monitoring of a complex ecological
system consists in observation (measurement) of certain state
variables, and the whole state process has to be determined from the
observed data. The solution proposed in the paper is the design of an
observer system, which makes it possible to approximately recover
the state process from its partial observation. The method is
illustrated with a trophic chain of resource – producer – primary
consumer type and a numerical example is also presented.
[1] Metz, J. A. J. 1977. State space model for animal behaviour. Ann. Syst.
Res. 6: 65-109.
[2] Metz, J. A. J. and Dickmann O. (Eds), 1986. The Dinamics of
Physiologically structured Populations, Springer Lecture Notes in
Biomath. 68.
[3] Kalman, R. E., Falb, P. L., Arbib, M. A., 1969. Topics in Mathematical
System Theory. McGraw-Hill, New York.
[4] Zadeh, L. A. and Desoer, C. A., 1963. Linear System Theory-The State
Space Approach, New York: McGraw-Hill Book Co.
[5] Chen, Ben M.; Lin, Zongli; Shamesh, Yacov A., 2004. Linear Systems
Theory. A Structural Decomposition Approach. Birkhauser, Boston.
[6] Lee, E.B. and Markus, L., 1971. Foundations of Optimal Control
Theory. New York-London-Sydney : Wiley.
[7] Varga, Z., Scarelli, A. and Shamandy, A., 2003. State monitoring of a
population system in changing environment. Community Ecology 4 (1),
73-78.
[8] López I, Gámez M, Molnár, S., 2007a. Observability and observers in a
food web. Applied Mathematics Letters 20 (8): 951-957.
[9] López, I., Gámez, M., Garay, J. and Varga, Z., 2007b. Monitoring in a
Lotka-Volterra model. Biosystems, 83, 68-74.
[10] Gámez, M., López, I. and Varga, Z., 2008. Iterative scheme for the
observation of a competitive Lotka-Volterra system. Applied
Mathematics and Computation. 201 811-818.
[11] Gámez, M.; López, I. and Molnár, S., 2008. Monitoring environmental
change in an ecosystem. Biosystems, 93, 211-217.
[12] Varga, Z., 2008. Applications of mathematical systems theory in
population biology. Periodica Mathematica Hungarica. 51 (1), 157-168.
[13] Shamandy, A., 2005. Monitoring of trophic chains. Biosystems, Vol. 81,
Issue 1, 43-48.
[14] Svirezhev, Yu.M. and D.O. Logofet (1983). Stability of biological
communities. Mir Publishers, Moscow.
[15] Jorgensen, S., Svirezhev, Y. (Eds.), 2004. Towards a Thermodynamic
Theory for Ecological Systems Pergamon
[16] Odum, E. P. 1971. Fundamentals of Ecology. 3rd ed. Saunders,
Philadelphia. 574 pp.
[17] Yodzis, P. (1989). Introduction to Theoretical Ecology. Harper & Row.
New York.
[18] Sundarapandian, V., 2002. Local observer design for nonlinear systems.
Mathematical and computer modelling 35, 25-36.
[1] Metz, J. A. J. 1977. State space model for animal behaviour. Ann. Syst.
Res. 6: 65-109.
[2] Metz, J. A. J. and Dickmann O. (Eds), 1986. The Dinamics of
Physiologically structured Populations, Springer Lecture Notes in
Biomath. 68.
[3] Kalman, R. E., Falb, P. L., Arbib, M. A., 1969. Topics in Mathematical
System Theory. McGraw-Hill, New York.
[4] Zadeh, L. A. and Desoer, C. A., 1963. Linear System Theory-The State
Space Approach, New York: McGraw-Hill Book Co.
[5] Chen, Ben M.; Lin, Zongli; Shamesh, Yacov A., 2004. Linear Systems
Theory. A Structural Decomposition Approach. Birkhauser, Boston.
[6] Lee, E.B. and Markus, L., 1971. Foundations of Optimal Control
Theory. New York-London-Sydney : Wiley.
[7] Varga, Z., Scarelli, A. and Shamandy, A., 2003. State monitoring of a
population system in changing environment. Community Ecology 4 (1),
73-78.
[8] López I, Gámez M, Molnár, S., 2007a. Observability and observers in a
food web. Applied Mathematics Letters 20 (8): 951-957.
[9] López, I., Gámez, M., Garay, J. and Varga, Z., 2007b. Monitoring in a
Lotka-Volterra model. Biosystems, 83, 68-74.
[10] Gámez, M., López, I. and Varga, Z., 2008. Iterative scheme for the
observation of a competitive Lotka-Volterra system. Applied
Mathematics and Computation. 201 811-818.
[11] Gámez, M.; López, I. and Molnár, S., 2008. Monitoring environmental
change in an ecosystem. Biosystems, 93, 211-217.
[12] Varga, Z., 2008. Applications of mathematical systems theory in
population biology. Periodica Mathematica Hungarica. 51 (1), 157-168.
[13] Shamandy, A., 2005. Monitoring of trophic chains. Biosystems, Vol. 81,
Issue 1, 43-48.
[14] Svirezhev, Yu.M. and D.O. Logofet (1983). Stability of biological
communities. Mir Publishers, Moscow.
[15] Jorgensen, S., Svirezhev, Y. (Eds.), 2004. Towards a Thermodynamic
Theory for Ecological Systems Pergamon
[16] Odum, E. P. 1971. Fundamentals of Ecology. 3rd ed. Saunders,
Philadelphia. 574 pp.
[17] Yodzis, P. (1989). Introduction to Theoretical Ecology. Harper & Row.
New York.
[18] Sundarapandian, V., 2002. Local observer design for nonlinear systems.
Mathematical and computer modelling 35, 25-36.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:49941", author = "I. López and J. Garay and R. Carreño and Z. Varga", title = "Observer Design for Ecological Monitoring", abstract = "Monitoring of ecological systems is one of the major
issues in ecosystem research. The concepts and methodology of
mathematical systems theory provide useful tools to face this
problem. In many cases, state monitoring of a complex ecological
system consists in observation (measurement) of certain state
variables, and the whole state process has to be determined from the
observed data. The solution proposed in the paper is the design of an
observer system, which makes it possible to approximately recover
the state process from its partial observation. The method is
illustrated with a trophic chain of resource – producer – primary
consumer type and a numerical example is also presented.", keywords = "Monitoring, observer system, trophic chain", volume = "3", number = "6", pages = "406-5", }