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Population dynamics is the type of mathematics used to model and study the size and age composition of populations as dynamical systems.Population dynamics is a branch of mathematical biology, and uses mathematical techniques such as differential equations to model behaviour.
Dynamic Amplification Factor (DAF) or Dynamic Increase Factor (DIF), is a dimensionless number which describes how many times the deflections or stresses should be multiplied to the deflections or stresses caused by the static loads when a dynamic load is applied on to a structure.
By now, it is a widely accepted view to analogize Malthusian growth in Ecology to Newton's First Law of uniform motion in physics. [ 8 ] Malthus wrote that all life forms, including humans, have a propensity to exponential population growth when resources are abundant but that actual growth is limited by available resources:
For example, with an annual growth rate of 4.8% the doubling time is 14.78 years, and a doubling time of 10 years corresponds to a growth rate between 7% and 7.5% (actually about 7.18%). When applied to the constant growth in consumption of a resource, the total amount consumed in one doubling period equals the total amount consumed in all ...
He applied the same mathematical formula to describe plant size over time. The equation for exponential mass growth rate in plant growth analysis is often expressed as: = Where: M(t) is the final mass of the plant at time (t). M 0 is the initial mass of the plant.
Dynamical systems theory and chaos theory deal with the long-term qualitative behavior of dynamical systems.Here, the focus is not on finding precise solutions to the equations defining the dynamical system (which is often hopeless), but rather to answer questions like "Will the system settle down to a steady state in the long term, and if so, what are the possible steady states?", or "Does ...
Growth like this is observed in real-life activity or phenomena, such as the spread of virus infection, the growth of debt due to compound interest, and the spread of viral videos. In real cases, initial exponential growth often does not last forever, instead slowing down eventually due to upper limits caused by external factors and turning ...
In econometrics, a dynamic factor (also known as a diffusion index) is a series which measures the co-movement of many time series. It is used in certain macroeconomic models. A diffusion index is intended to indicate the changes of the fraction of economic data time series which increase or decrease over the selected time interval,