The Lotka-Volterra competition equations with periodic coefficients derived from the MacArthur-Levins theory of a one-dimensional resource niche are studied when the parameters are allowed to oscillate periodically in time. Specifically, niche positions and widths, resource availability and resource consumption rates are allowed small amplitude periodicities around a specified mean value. Two o...

Trofik merupakan tingkatan yang menggambarkan cara suatu spesies memperoleh energi dari lingkungan. Jalur perpindahan trofik satu ke lain dikenal sebagai rantai makanan kemudian saling menjalin menjadi jaring-jaring makanan. Dalam makalah ini dibahas pemodelan matematika dua pada pemangsa generalis, yaitu dapat memakan beberapa jenis mangsa. Model dikembangkan berdasarkan model mangsa Lotka-Vol...

Two-dimensional informetrics is defined in the general context of sources that produce items and examples are given. These systems are called “Information Production Processes” (IPPs). They can be described by a size-frequency function f or, equivalently, by a rank-frequency function g. If f is a decreasing power law then we say that this function is the law of Lotka and it is equivalent with t...

Apart from interacting, prey and predators may also avoid each other by moving into refuges where they lack food, yet survive by switching to an energy-saving physiological state. Lotka-Volterra models of predator-prey interactions ignore this option. Therefore, we have modelled this game of 'joining versus opting out' by extending Lotka-Volterra models to include portions of populations not in...

The study examines temporal trends in population abundance and distribution of a predator and prey species using a spatial diffusion model. Using Chebyshev Spectral Methods in MATLAB®, we were able to develop a model composed of two partial differential equations to simulate and predict population growth and range expansion for the two species. The foundation of the modeling program is a diffus...

This work investigated the stability of some Lotka-Volterra type models. We used the Liapunov method, which consists in analyzing the stability of systems of ordinary differential equations (ODE's), around the equilibrium, when submitted to perturbations in the initial conditions.

The dynamic economic behavior in most integrated assessment models linking economic growth to climate change involves a differential equation solved by Jacob Bernoulli in 1695. Using the dynamic integrated climate economy (DICE) model and freezing exogenous variables at initial values, this dynamic is shown to produce implausible projections on a 60-year time frame. If world capital started at ...

We consider a bitrophic spatially distributed community consisting of prey and actively moving predators. The model is based on the assumption that the spatial and temporal variations of the predators' velocity are determined by the prey gradient. Locally, the populations follow the simple Lotka-Volterra interaction. We also assume predator reproduction and mortality to be negligible in compari...

where x1(t) and x2(t) are real functions of time; x0 i:=dxi/dt; and a, b, c are positive real constants. This system was originally introduced by Lotka [1] in 1920 as a model of undamped oscillations in autocatalytic chemical reactions, and was later applied by Volterra [2] to treat predatorprey interactions in ecology. Other applications have followed in the intervening years in physics [3], c...

Archaeologists argue that the replacement of Neanderthals by modern humans was driven by interspecific competition due to a difference in culture level. To assess the cogency of this argument, we construct and analyze an interspecific cultural competition model based on the Lotka-Volterra model, which is widely used in ecology, but which incorporates the culture level of a species as a variable...