Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Modeling with Differential Equations01:25

Modeling with Differential Equations

289
Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
289
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

414
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
414
Pharmacodynamic Models: Logarithmic Concentration–Effect Model01:15

Pharmacodynamic Models: Logarithmic Concentration–Effect Model

99
The log-linear model is a pharmacological framework used to describe the relationship between drug concentration and its effect. This model is particularly relevant when the observed effects range between 20% and 80% of the drug’s maximum effect (Emax), where a near-linear relationship is observed between the log of drug concentration and the measured effect. However, the log-linear model does not predict the maximum possible effect (Emax) or the effect at zero drug concentration,...
99
Types of Functions III01:28

Types of Functions III

386
Logarithmic and piecewise functions play central roles in mathematical modeling, particularly when capturing nonlinear or segmented behaviors in real-world phenomena. Although these functions differ fundamentally in structure and application, both serve to represent complex relationships in simplified mathematical terms.A logarithmic function is defined as the inverse of an exponential function, expressed as These functions grow quickly for small values of x but slow down as x increases,...
386
Exponential Equations with Logarithms: Problem Solving01:29

Exponential Equations with Logarithms: Problem Solving

261
In ecological studies, exponential models are often used to predict how populations grow over time under favorable conditions. These models assume that the growth rate is proportional to the current population, leading to continuous and compounding increases.The model expresses the population as a function of time, combining the initial population with a growth factor raised to an exponent involving the growth rate and time. To estimate how long it takes for a population to reach a specific...
261
Probability Distributions01:32

Probability Distributions

13.7K
 The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson...
13.7K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Design and control of soft biomimetic pangasius fish robot using fin ray effect and reinforcement learning.

Scientific reports·2022
Same author

Plant Tissue Modelling Using Power-Law Filters.

Sensors (Basel, Switzerland)·2022
Same author

A generalized framework for elliptic curves based PRNG and its utilization in image encryption.

Scientific reports·2022
Same author

Plant stem tissue modeling and parameter identification using metaheuristic optimization algorithms.

Scientific reports·2022
Same author

Correction to: Modified fractional-order model for biomass degradation in an up-flow anaerobic sludge blanket reactor at Zenein Wastewater Treatment Plant.

Environmental science and pollution research international·2022
Same author

Modeling of Soft Pneumatic Actuators with Different Orientation Angles Using Echo State Networks for Irregular Time Series Data.

Micromachines·2022
Same journal

Piezo1 inhibition promoted MELK degradation and impeded influenza virus entry into host cells.

Journal of advanced research·2026
Same journal

PDD-mediated mitochondrial and chloroplast tRNA modifications regulate cellular protein synthesis by shaping the genome-wide translational landscape in rice.

Journal of advanced research·2026
Same journal

Natural variation in GmSW6 regulates seed weight and quality in soybean.

Journal of advanced research·2026
Same journal

A multi-trait polygenic risk score enhances osteoporosis risk prediction in East Asian population.

Journal of advanced research·2026
Same journal

Akkermansia muciniphila-derived postbiotics reprogram immune balance to combat sepsis via the IDO1/Kyn/AhR metabolic axis.

Journal of advanced research·2026
Same journal

A mineral-electron-driven photophosphorylation has potential impacts on photosynthetic bacteria evolution and ecological environment changes.

Journal of advanced research·2026
See all related articles

Related Experiment Video

Updated: Apr 17, 2026

Tactile Semiautomatic Passive-Finger Angle Stimulator TSPAS
04:40

Tactile Semiautomatic Passive-Finger Angle Stimulator TSPAS

Published on: July 30, 2020

3.4K

On some generalized discrete logistic maps.

Ahmed G Radwan1

  • 1Engineering Mathematics Department, Faculty of Engineering, Cairo University, 12613, Egypt.

Journal of Advanced Research
|February 17, 2015
PubMed
Summary
This summary is machine-generated.

This study introduces generalized logistic maps with arbitrary powers, enhancing flexibility beyond conventional models. These versatile maps offer improved control for applications in modeling and security.

Keywords:
Arbitrary powerBifurcation diagramChaosGeneralized 1D mapLogistic mapStability

Related Experiment Videos

Last Updated: Apr 17, 2026

Tactile Semiautomatic Passive-Finger Angle Stimulator TSPAS
04:40

Tactile Semiautomatic Passive-Finger Angle Stimulator TSPAS

Published on: July 30, 2020

3.4K

Area of Science:

  • Dynamical Systems and Chaos Theory
  • Mathematical Modeling

Background:

  • Conventional logistic maps are crucial for modeling and security but limited by a single parameter.
  • This limitation restricts their adaptability in complex applications.

Purpose of the Study:

  • To introduce novel generalized logistic maps with arbitrary powers.
  • To enhance the flexibility and applicability of logistic maps for diverse systems.
  • To demonstrate that conventional logistic maps are a special case of the proposed generalized maps.

Main Methods:

  • Development of three distinct generalized logistic map equations incorporating arbitrary powers.
  • Analysis of the impact of the arbitrary power parameter on system dynamics.
  • Investigation of equilibrium points, stability conditions, and bifurcation diagrams.

Main Results:

  • The generalized maps offer increased degrees of freedom and versatile responses.
  • The arbitrary power parameter significantly influences the number, location, and stability of equilibrium points.
  • Bifurcation analysis reveals the potential for chaotic behavior with parameter adjustments.

Conclusions:

  • The proposed generalized logistic maps provide a more flexible and adaptable framework than conventional maps.
  • The arbitrary power parameter allows for fine-tuning system behavior for specific applications.
  • These enhanced maps represent a significant advancement for complex modeling and security systems.