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Everything about Functional square root
Function that, applied twice, gives another function
In mathematics, a functional square root (sometimes called a half iterate) is a square root of a function with respect to the operation of function composition. In other words, a functional square root of a function g is a function f satisfying f(f(x)) = g(x) for all x. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Functional square rootA 5-minute orientation
- Skim a recent paper: The dynamics of a delayed predator-prey model with square root functional response and stage structureInfluential work since 2022
- Pick up a classic book: Algebra 2The most-reprinted book on the subject
- Read the landmark paper: Predator–prey dynamics with square root functional responsesCited 216 times
- Go sideways: Iterated functionA closely related topic
- Go sideways: Schröder's equationA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Predator–prey dynamics with square root functional responses
Reciprocation, square root, inverse square root, and some elementary functions using small multipliers
Predator–Prey Dynamical Behavior and Stability Analysis with Square Root Functional Response
Generalization of functional equation for the square root spiral
Stability of a functional equation for square root spirals
Fear effect in discrete prey-predator model incorporating square root functional response
A Prey-Predator Dynamics with Square Root Functional Responses and Strong Allee Effect
On a Predator-Prey Model with Square Root Functional Response
🆕 Influential since 2022
The dynamics of a delayed predator-prey model with square root functional response and stage structure
Transient Dynamics Analysis of a Predator-Prey System with Square Root Functional Responses and Random Perturbation
Stability Analysis of Fractional-Order Predator-Prey System with Square Root Functional Response
Small Area Estimation under Square Root Transformed Fay-Herriot Model with Functional Measurement Error in Covariates
Dynamics and Strong Resonance Bifurcations in a Discrete Predator–Prey Model With Square Root Functional Response
📚 Books worth reading
Algebra 2McGraw-Hill · 1998- 📕Square roots of an orthogonal matrixErold Wycliffe Hinds · 1971
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Iterated function In mathematics, an iterated function is a function that is obtained by composing another function with itself two or several times. The process of repeatedly…
- Schröder's equation Schröder's equation, named after Ernst Schröder, is a functional equation with one independent variable: given the function h, find the function Ψ such…
- Half-exponential function In mathematics, a half-exponential function is a functional square root of an exponential function. That is, a function f such that f composed with itself…
- Functional equation In mathematics, a functional equation is, in the broadest meaning, an equation in which one or several functions appear as unknowns. So, differential equations…
- Function composition In mathematics, the composition operator ∘ takes two functions, f and g, and returns a new function f∘g. When the composite function f∘g (pronounced "f…
- Abel equation The Abel equation, named after Niels Henrik Abel, is a type of functional equation of the form f(h(x))=h(x+1) or α(f(x))=α(x)+1. The forms are equivalent…
- Superfunction In mathematics, superfunction is a nonstandard name for an iterated function for complexified continuous iteration index. Roughly, for some function f…
- Tetration In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. There is no universal notation for tetration, though…