A general system of high-order differential equations describing complex dynamics of replicating biomolecules is given. Symmetry relations and coordinate transformations of general replication systems leading to topologically equivalent systems are derived. Three chaotic attractors observed in Lotka-Volterra equations of dimension n = 3 are shown to represent three cross-sections of one and the...

Q -conditional symmetries of the classical diffusive Lotka–Volterra system in the case of one space variable are completely described and a set of such symmetries in explicit form is constructed. The relevant non-Lie ansatz to reduce the diffusive Lotka–Volterra systems with correctly specified coefficients to ODE systems and examples of new exact solutions are found. A possible biological inte...

This paper examines the process and final result of extending the basic Lotka-Volterra predator-prey model to include different age groups within each population. Basic analysis of the results were performed to determine the relevance of the proposed extension. Calculations and graphing were handled with MatLab. The natural outcome of the model should be either a periodic cycle about an equilib...

In the present paper a generalized Lotka-Volterra food chain system has been studied and also its dynamic behavior such as locally asymptotic stability has been analyzed in case of existing interspecies competition. Furthermore, it has been shown that the said system is permanent (in the sense of boundedness and uniformly persistent). Finally, it is proved that the nontrivial equilibrium point...

In this paper we stochastically perturb the delay Lotka–Volterra model ẋ(t)= diag(x1(t), . . . , xn(t))[A(x(t)− x̄)+B(x(t − τ )− x̄)] into the stochastic delay differential equation (SDDE) dx(t)= diag(x1(t), . . . , xn(t)){[A(x(t)− x̄)+B(x(t − τ )− x̄)]dt + σ (x(t)− x̄)dw(t)}. The main aim is to reveal the effects of environmental noise on the delay Lotka–Volterra model. Our results can essentially ...

some scientists are interesting to study in area of harvested ecological modelling. the harvested population dynamics is more realistic than other ecological models. in the present paper, some of the lotka-volterra predator-prey models have been considered. in the said models, existing species are harvested by constant or variable growth rates. the behavior of their solutions has been analyzed ...

the food chain refers to a natural system by which energy is transmitted from one organism to another. in fact, a food chain consists of producers, consumers and decomposition. presence of complex food web increase the stability of the ecosystem. classical food chain theory arises from lotka-volterra model. in the present paper, the dynamics behavior of three level food chain is studied. a syst...

Generalized matrix Lotka-Volterra lattice equations are obtained in a systematic way from a “master equation” possessing a bicomplex formulation.

scientists are interested in find out “how to use living resources without damaging the ecosystem at the same time?” from nineteen century because the living resources are limited. thus, the harvested rate is used as the control parameters. moreover, the study of harvested population dynamics is more realistic.    in the present paper, some predator-prey models in which two ecologically interac...

The concept of a stable population was first intro?uced into demography by Alfred J. Lotka 1 as a partIcular case of a Malthusian population. Lotka went on to demonstrate that a stable population could also be considered as a limit state towards which populations with unchanging mortality and fertility tended, and it is primarily this second aspect which has received attention from demographers...