China
Africa
Explore chapters and articles related to this topic
The Emergence of Temporal Order in the Economy
Published in Pier Luigi Gentili, Untangling Complex Systems, 2018
The system of equations [6.15] and [6.16] is formally equivalent to the Lotka-Volterra equations describing the predator-prey dynamics in a natural ecosystem. This is evident if we arrange [6.15] and [6.16] in the following form: [] dμdt=(1κ−θ−n)μ−μvκ [] dvdt=βμv−(α+θ)v
Leveraging Deterministic Chaos to Mitigate Combinatorial Explosions
Published in Larry B. Rainey, Mo Jamshidi, Engineering Emergence, 2018
Predator-prey or Lotka-Volterra equations are nonlinear first order differential equations that have been used to represent where an interdependency exists between the populations of two or more species, e.g., rabbits and foxes. This dependency causes the behaviors of the equation to produce a sinusoidal phase-shifted relationship between predator and prey. Under certain conditions of population growth, it can produce an emergent aspect, where the population of one group varies in a non-uniform aspect to the other group. A predator population may sporadically increase after the prey population increases and decrease when the prey is killed off. In this instance, variation in population sizes may not necessarily be cyclical, but may vary chaotically.
Introduction to Physiological Regulators and Control Systems
Published in Robert B. Northrop, Endogenous and Exogenous Regulation and Control of Physiological Systems, 2020
The nonlinear ODEs below are a form of the Lotka–Volterra equations which can be used to model predator–prey interactions in an oversimplified ecosystem. x and y are the population densities of the two competing species. x˙=x(a−by)y˙=y(cx−d)
Emergent behavior in the battle management system
Published in Applied Artificial Intelligence, 2022
Aleksandar Seizovic, David Thorpe, Steven Goh
In mathematics the Lanchester (1999) presented a collection of joined ordinary differential equations known as the Lanchester equations (LEs); the roots of the LEs are process models for reducing strength or effectiveness in modern warfare (Engel and Gass 2001). They are a collection of differential equations describing the time dependence of the strengths of two armies, A (green force) and B (red force), as a function of time, c2n22 = c1n. Thus, the fighting strengths of both forces are equal when the products of the squares of the numerical strengths times the coefficients of effectiveness are equal (Chen et al. 2011). Osipov and Maksimov (2018) independently devised a series of differential equations known as Lanchester’s Square Law (Engel and Gass 2001) to demonstrate the power relationships between opposing forces. With the design and development of BMS complex systems, understanding differential equations is important. The Lotka-Volterra equations (Lanchester 1999) are used to model the dynamics of interacting “predator-prey populations” (Washburn et al. 2016).
Some reflections on defects in liquid crystals: from Amerio to Zannoni and beyond
Published in Liquid Crystals, 2018
The mathematical sciences of the present day contain many references to Volterra’s name. There are (different) Volterra processes in material science and in control theory, as well as Volterra integral equations and integro-differential equations in the theory of elastic media and indeed on the pages of every textbook on integral equations. The Lotka–Volterra equations appear almost on the first page of any contemporary treatise on theoretical ecology, sometimes disguised as the Volterra population equation. Elsewhere, we find Volterra systems, Volterra series, Volterra operators, Volterra kernels, Volterra filters, Volterra spaces and Volterra functionals. His astronomical work is celebrated by the Volterra crater in the northern hemisphere of the far side of the moon. His name has even leaked out of the mathematical into the commercial world. For in London, Volterra Consulting will (presumably for a suitably gigantic fee, although I have to admit I have been too shy to ask) use mysterious quantitative methods to read the economic runes and help you thereby to run your company.