Geodesic
Stabilization and vitality in ecological models. Formation process of passive states
Matematičeskoe modelirovanie, Tome 21 (2009) no. 8, pp. 3-20.

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We formalize the individual biological transition process from an active to a passive state under unfavor-able environment conditions. From the mathematical point of view this leads to an universal linear super-structure over nonlinear ecological system models. We infer that under a special choice of transition ve-locities there is a possibility of oscillatory instability stabilization and of an increasing of populations vital-ity. The correct models of adaptation of biological coefficients in variable environment, taking into ac-count the “active state–passive state” interchange are offered. In the model “prey–predator” the cycle movement (chasing–escape) within the space of parameters is revealed. 
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V. G. Il'ichev. Stabilization and vitality in ecological models. Formation process of passive states. Matematičeskoe modelirovanie, Tome 21 (2009) no. 8, pp. 3-20. http://geodesic.mathdoc.fr/item/MM_2009_21_8_a0/

[1] Ushakov B. P., “Evolyutsionnoe znachenie temperaturnykh adaptatsii zhivotnykh”, Uspekhi sovremennoi biologii, 93:2 (1982), 302–309 | MR

[2] Ushatinskaya R. S., Skrytaya zhizn i anabioz, Nauka, M., 1990, 182 pp.

[3] Getsina R. P., Ilichev V. G., “Passivnaya forma suschestvovaniya – stabiliziruyuschii faktor v dinamike vzaimodeistvuyuschikh populyatsii”, Izv. Sev.-Kav. Nauch. Tsentra Vyssh. Shk. Estestv. Nauki, 1986, no. 3, 131–136

[4] Ilichev V. G., “Mekhanizm obrazovaniya passivnykh sostoyanii i stabilizatsiya dinamicheskikh sistem”, Kibernetika i sistemnyi analiz, 1995, no. 3, 128–137 | MR

[5] Ilichev V. G., “Struktura semeistva obratnykh svyazei i ustoichivost ekologicheskikh sistem”, Avtomatika i Telemekhanika, 1986, no. 12, 66–76 | MR

[6] Ilichev V. G., “O tekhnologii postroeniya imitatsionnykh modelei ekologicheskikh sistem. Mekhanizmy adaptatsii”, Matemat. modelirovanie, 4:3 (1992), 11–19 | MR

[7] Ilichev V. G., Ilicheva O. A., “Analiz modelei konkurentsii v postoyannoi i periodicheskoi srede”, Matemat. modelirovanie, 14:3 (2002), 71–83 | MR | Zbl

[8] Ilichev V. G., Ilicheva O. A., Voronin V. Yu., “Kriterii otbora v sistemakh ‘vse protiv vsekh’ i ‘vse protiv odnogo’ ”, Obozrenie prikl. i promysh. matematiki, 6:2 (1999), 311–317

[9] Ilichev V. G., “Delta-funktsii i issledovanie ekologicheskikh modelei Volterra v peremennoi srede”, Izv. Vuzov. Matematika, 1998, no. 4, 23–33 | MR

[10] Troyan P., Faktorialnaya ekologiya, Vischa Shkola, Kiev, 1989, 232 pp.

[11] Contois D. E., “Kinetics of bacterial growth relationship between population dessity and specific growth rate of continuous culture”, J. Gen. Microbiol., 1959, no. 1–2, 40

[12] Ilichev V. G., “Adaptatsiya parametrov v modelyakh populyatsii”, Zhurnal Obschei Biologii, 66:2 (2005), 171–179 | MR

[13] Ilichev V. G., “Globalnye svoistva neavtonomnykh dinamicheskikh sistem i ikh prilozhenie v modelyakh konkurentsii”, Izv. RAN. Teoriya i sistemy upravleniya, 41:5 (2002), 677–684 | MR

[14] Opoitsev V. I., Nelineinaya sistemostatika, Nauka, M., 1986, 247 pp. | MR