Conference publications

Abstracts

XIV conference

Coexistance of Attractors in the Agricultural Ecosystem, which Includes Genetically Modified Organisms: Mathematical Modeling

Gonik M.M., Medvinsky A.B., Li B.-L.¹, Malchow H.²

Institute for Theoretical and Experimental Biophysics, Russia, 142290, Pushchino, Moscow Region, Institutskya str. 3, phone: (4967)739157, email: medvinsky@iteb.ru, mgmaria@yandex.ru

¹University of California, USA, California, 92507, Riverside.

²Institute of Environmental Systems Research, University of Osnabrueck, Germany, 49069, Osnabrueck, Germany.

1 pp.

A modification of the model of an agricultural ecosystem [1], which includes genetically modified insecticidal Bt-plants is presented. Insect density is taken to be high, so that the insects fecundity dependence on the abundance of the insects is exponential, in contrast to the hyperbolic dependence [1], which is typical for low insect densities [2]. We study the plant-insect dynamics under invasion of mutant insects. Two types of mutant insects are perceived to appear: (1) insects, which carry genes of resistance to Bt-toxin and (2) the transition type, which possesses the genes of resistance as well as of susceptibility to Bt-toxin. The allele of resistance is recessive. It is shown that in contrast to the system, which is characterized by a hyperbolic insects fecundity dependence on the insect abundance [1], a chaotic attractor does not arise in the model agricultural system with an exponential insects fecundity dependence on the insect abundance. By contrast, coexistence of non-chaotic attractors with different amplitude characteristics occurs.