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The Lotka–Volterra system of equations is an example of a Kolmogorov population model (not to be confused with the better known Kolmogorov equations), [2] [3] [4] which is a more general framework that can model the dynamics of ecological systems with predator–prey interactions, competition, disease, and mutualism.
He described an effect in six predator–prey models where increasing the food available to the prey caused the predator's population to destabilize. A common example is that if the food supply of a prey such as a rabbit is overabundant, its population will grow unbounded and cause the predator population (such as a lynx) to grow unsustainably ...
The model was particularly inspired by the work of Italian physicist Vito Volterra, who had developed his predator-prey equations based on observations of fish populations in the Adriatic Sea during World War I. Volterra's work showed that during the war, when fishing was reduced due to military activities, the proportion of predator fish ...
When all prey species are at equal densities, the predator will indiscriminately select between prey species. However, if the density of one of the prey species decreases, then the predator will start selecting the other, more common prey species with a higher frequency because if it can increase the efficiency which with it captures the more ...
a = conversion efficiency: the fraction of prey energy assimilated by the predator and turned into new predators P = predator density V = prey density m = predator mortality c = capture rate Demographic response consists of a change in dP/dt due to a change in V and/or m. For example, if V increases, then predator growth rate (dP/dt) will increase.
The solution to these equations in the simple one-predator species, one-prey species model is a stable linked oscillation of population levels for both predator and prey. However, when time lags between respective population growths are modeled, these oscillations will tend to amplify, eventually leading to extinction of both species.
The 1987 film Predator is an example of prey-reversal where the victim becomes the predator. Armed with a stealth suit and ultimate high-tech gear, the predator methodically dispatches the humans that find themselves in the jungle.
Example: Let α −2 = 0.451, α −1 = 0.5, and α 2 = 0.237. If α 1 = 0.5 then all eigenvalues are negative and the only attractor is a fixed point. If α 1 = 0.852 then the real part of one of the complex eigenvalue pair becomes positive and there is a strange attractor. The disappearance of this Lyapunov function coincides with a Hopf ...