Observer design for open and closed trophic chains

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. Such systems-theoretical approach has been applied before by the authors to Lotka–Volterra type population systems. In the present paper this methodology is extended to a non-Lotka–Volterra type trophic chain of resource–producer–primary consumer type and numerical examples for different observation situations are also presented.

[1]  Charles A. Desoer,et al.  Linear System Theory: The State Space Approach , 2008 .

[2]  R. E. Kalman,et al.  Linear system theory-The state space approach , 1965 .

[3]  I. Lópeza,et al.  Monitoring in a Lotka – Volterra model , 2006 .

[4]  S. Levin Lectu re Notes in Biomathematics , 1983 .

[5]  Dmitriĭ Olegovich Logofet,et al.  Stability of Biological Communities , 1983 .

[6]  Ali Shamandy Monitoring of trophic chains. , 2005, Bio Systems.

[7]  Sándor Molnár,et al.  Observability and observers in a food web , 2007, Appl. Math. Lett..

[8]  Manuel Gámez,et al.  Observer design for phenotypic observation of genetic processes , 2008 .

[9]  S. Jørgensen,et al.  Towards a Thermodynamic Theory for Ecological Systems. , 2005 .

[10]  E. Odum Fundamentals of Ecology. , 1955 .

[11]  E B Lee,et al.  Foundations of optimal control theory , 1967 .

[12]  J. G. Navarro On observability of Fisher's model of selection , 1992 .

[13]  Zoltán Varga Applications of mathematical systems theory in population biology , 2008, Period. Math. Hung..

[14]  P. Yodzis,et al.  Introduction to Theoretical Ecology , 1989 .

[15]  Sándor Molnár,et al.  Monitoring environmental change in an ecosystem , 2008, Biosyst..

[16]  Zoltán Varga,et al.  Iterative scheme for the observation of a competitive Lotka-Volterra system , 2008, Appl. Math. Comput..

[17]  Michael A. Arbib,et al.  Topics in Mathematical System Theory , 1969 .

[18]  O. Diekmann,et al.  The Dynamics of Physiologically Structured Populations , 1986 .

[19]  E. Odum Fundamentals of ecology , 1972 .

[20]  Hans A. J. Metz,et al.  State Space Models for Animal Behaviour , 1977 .

[21]  B. M. Chen,et al.  INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL Int. J. Robust Nonlinear Control 2006; 16:281–285 Published online in Wiley InterScience (www.interscience.wiley.com) BOOK REVIEWS linear systems theory: a structural decomposition , 2006 .

[22]  V. Sundarapandian Local observer design for nonlinear systems , 2002 .