The logistic map is only a second-degree polynomial ; the horseshoe map is piecewise linear.

The logistic map for 100 generations of x ( plotted left to right ) as r moves from 0 to 4

The map was popularized in a seminal 1976 paper by the biologist Robert May, in part as a discrete-time demographic model analogous to the logistic equation first created by Pierre François Verhulst.

Mathematically, the logistic map is written

However, as a demographic model the logistic map has the pathological problem that some initial conditions and parameter values lead to negative population sizes.

The r = 4 case of the logistic map is a nonlinear transformation of both the bit shift map and the case of the tent map.

Bifurcation diagram of the logistic map

An example is the bifurcation diagram of the logistic map:

For systems such as the logistic map, the bifurcation diagram shows a range of parameter values for which apparently the only cycle has period 3.

Interestingly, the above " Sharkovskii ordering " of the positive integers also occurs in a slightly different context in connection with the logistic map: the stable cycles appear in this order in the bifurcation diagram, starting with 1 and ending with 3, as the parameter is increased.

Examples of nonlinear recurrence relations are the logistic map and the relations that define the various Hofstadter sequences.

An example of a recurrence relation is the logistic map:

* Dr. Ronald Joe Record's mathematical recreations software laboratory includes an X11 graphical client, lyap, for graphically exploring the Lyapunov exponents of a forced logistic map and other maps of the unit interval.

* is called the factored form, where and are the roots of the quadratic equation, it is used in logistic map

As a dynamical system, the canonical Hénon map is interesting because, unlike the logistic map, its orbits defy a simple description.

Although the continuous-time logistic equation is often compared to the logistic map because of similarity of form, it is actually more closely related to the Beverton – Holt model of fisheries recruitment.

From left to right: uncorrelated stochastic data ( white noise ), harmonic oscillation with two frequencies, chaotic data with linear trend ( logistic map ) and data from an autoregressive process | auto-regressive process.

Bifurcation diagram of the logistic map.

The logistic map is a prominent example of the mappings that Feigenbaum studied in his noted 1978 article: Quantitative Universality for a Class of Nonlinear Transformations.

) Whatever philosophy is conceived to be, its rationalist, logistic attitude to evidence should make it clear that it is something other than science.

The command's mission is " To provide logistic support to operational forces forward deployed to the Indian Ocean and Persian Gulf AORs in support of national policy objectives.

According to Technorati, the number of blogs doubles about every 6 months with a total of 35. 3 million blogs. This is an example of the early stages of logistic growth, where growth is approximately exponential, since blogs are a recent innovation.

* The development of the chaotic behavior of the logistic sequence as the parameter r varies from approximately 3. 5699 to approximately 3. 8284 is sometimes called the Pomeau – Manneville scenario, which is characterized by a periodic ( laminar ) phase interrupted by bursts of aperiodic behavior.

A slightly more realistic and largely used population growth model is the logistic function, and its extensions.

For example, naive Bayes and linear discriminant analysis are joint probability models, whereas logistic regression is a conditional probability model.

In conjunction with modern logistic systems ( where the SP gun's systems can track and report on ammunition consumption and levels ) with similar navigation systems and palletized load dropping / lifting capabilities mean that the rapid displacement can occur without significant disruption to actually firing missions as it is possible for the ammunition to keep up with the guns.

In war, the word is used to describe the activity of an individual or group not associated with the military of the parties at war ( such as a foreign agent or an indigenous supporter ), in particular when actions result in the destruction or damaging of a productive or vital facility, such as equipment, factories, dams, public services, storage plants or logistic routes.

Although it is called the Trinidad & Tobago Regiment, the TTR is in fact structured more like a light infantry brigade, with a pair of infantry battalions, plus engineering and logistic support units:

In telecommunication, endurability is the property of a system, subsystem, equipment, or process that enables it to continue to function within specified performance limits for an extended period of time, usually months, despite a severe natural or man-made disturbance, such as a nuclear attack, or a loss of external logistic or utility support.

Collegio Ghislieri is a 450 years old Italian institution committed to promote University studies on the basis of merit, hosting around 200 pupils ( males and females ) who attend all faculties in Pavia State University, offering them logistic and cultural opportunities such as scholarships, lectures, conferences, a 100, 000 volumes library ( the third one among private libraries in Northern Italy ), foreign languages courses.

Mutualism is in essence the logistic growth equation + mutualistic interaction.

If security depends on keeping that secret, then disclosure leads to major logistic difficulties in developing, testing, and distributing implementations of a new algorithm: it is " brittle.

The Commandant of the Royal Palaces is mainly in charge, in close cooperation with the Chief of Protocol, of the logistic support of activities and the maintenance and cleaning of the Palaces, Castles and Residences.

HMI is usually linked to the SCADA system's databases and software programs, to provide trending, diagnostic data, and management information such as scheduled maintenance procedures, logistic information, detailed schematics for a particular sensor or machine, and expert-system troubleshooting guides.

Integrated Logistics Support ( ILS ) is a discipline used in military industries to ensure an easily supportable system with a robust customer service ( logistic ) concept at the lowest cost and in line with ( often high ) reliability, availability, maintainability and other requirements as defined for the project.

More recently, however, it was demonstrated that, using standard polynomial approximations to the normal cdf, the normal-ogive model is no more computationally demanding than logistic models.

A logistic function or logistic curve is a common sigmoid curve, given its name in 1844 or 1845 by Pierre François Verhulst who studied it in relation to population growth.

Despite the overwhelming military and logistic superiority of the Spanish Armed Forces based in Western Sahara in relation to the Moroccan Armed Forces, the Spanish government feared that the conflict with Morocco could lead to an open colonial war in Africa, which could put Franco's regime into question and lead to an abupt political change or a social instability and disaster.

Starting in 2012, HEC Montréal offers a master's degree entirely taught in English with courses covering international business networks, logistic systems, transportation systems, decision support tools, distribution, network optimization and the core " Economics and corporate organization " course.

The study found a positive logistic correlation between evapotranspiration in mm / yr and above-ground net primary production in g / m < sup > 2 </ sup >/ yr.

Therefore, it is inappropriate to think of R < sup > 2 </ sup > as a proportionate reduction in error in a universal sense in logistic regression.

Equation 1. 2 is the usual way in which logistic growth is represented mathematically and has several important features.

Given two populations, x < sub > 1 </ sub > and x < sub > 2 </ sub >, with logistic dynamics, the Lotka – Volterra formulation adds an additional term to account for the species ' interactions.