Relearchers apply dynamics system theory to predator-prey interactions

Oct 11, 2012
The mathematics behind predator-prey interactions
Credit: Thinkstock

European scientists advanced an important field of mathematics describing the behaviour of numerous physical and biological systems.

theory (DST) is a branch of mathematics devoted to describing the behaviour of complex physical and biological systems that change with the passage of time. In fact, the state of a dynamical system at any time is described by a fixed mathematical rule.

The fundamental utility of DST is that one may clearly state the immediate future state or possible states of a system based on the present state using the rule. When only one possible future state exists, the system is deterministic; when more than one possibility exists, the system is stochastic or random.

DST is relevant to many different fields including economics, biology and astrophysics. It has recently been applied to modelling athletic performance, human development, predator-prey dynamics and even limb regeneration in insects.

In DST, the so-called state space is defined as an n-dimensional vector space (similar to a three-dimensional (3D) Cartesian space) that describes the state of the system at any given time. Using the evolution law, one may determine the next state of all parameters.

Bifurcation theory describes the situation when a small perturbation in a parameter produces a large (qualitative) change in the system's behaviour.

initiated the Quribius project to address certain as yet unexplored topics in this field. Among the important Quribius project results, scientists produced a wealth of new bifurcation diagrams resulting from a specific bifurcation and carried out an exhaustive study of another type of dynamical system subjected to various .

Given the widespread application of DST, mathematical advances achieved by the Quribius team in describing dynamical systems should have important impact on many fields.EU-funded scientists advanced an important field of mathematics describing the behaviour of numerous physical and biological systems.

Dynamical systems theory (DST) is a branch of mathematics devoted to describing the behaviour of complex physical and that change with the passage of time. In fact, the state of a dynamical system at any time is described by a fixed mathematical rule.

The fundamental utility of DST is that one may clearly state the immediate future state or possible states of a system based on the present state using the rule. When only one possible future state exists, the system is deterministic; when more than one possibility exists, the system is stochastic or random.

DST is relevant to many different fields including economics, biology and astrophysics. It has recently been applied to modelling , human development, predator-prey dynamics and even in insects.

In DST, the so-called state space is defined as an n-dimensional vector space (similar to a three-dimensional (3D) Cartesian space) that describes the state of the system at any given time. Using the evolution law, one may determine the next state of all parameters.

Bifurcation theory describes the situation when a small perturbation in a parameter produces a large (qualitative) change in the system's behaviour.

European researchers initiated the Quribius project to address certain as yet unexplored topics in this field. Among the important Quribius project results, scientists produced a wealth of new bifurcation diagrams resulting from a specific bifurcation and carried out an exhaustive study of another type of dynamical system subjected to various perturbations.

Given the widespread application of DST, mathematical advances achieved by the Quribius team in describing dynamical systems should have important impact on many fields.

Explore further: 'Moral victories' might spare you from losing again

add to favorites email to friend print save as pdf

Related Stories

Advances in mathematical description of motion

May 29, 2012

Complex mathematical investigation of problems relevant to classical and quantum mechanics by EU-funded researchers has led to insight regarding instabilities of dynamic systems. This is important for descriptions ...

Periodic heart rate decelerations in premature infants

Apr 22, 2010

A normal healthy heart beats at a variable rate with extraordinarily complex fluctuations across a wide range of time scales. Reduced complexity of heart rate has both clinical and dynamical significance - it may provide ...

The Big Bang versus the 'Big Bounce'

Jul 06, 2012

Two fundamental concepts in physics, both of which explain the nature of the Universe in many ways, have been difficult to reconcile with each other. European researchers developed a mathematical approach ...

Mathematics Unites The Heavens And The Atom

Sep 28, 2005

In recent years, mathematicians have discovered an almost perfect parallel between the motion of spacecraft through the solar system and the motion of atoms in a chemical reaction - a hidden unity that has led to innovative ...

Recommended for you

Ultra high definition TVs boost LG Display profit

2 hours ago

(AP)—LG Display Co. said profit for the April-June quarter more than doubled as a stronger won reduced the value of its foreign debt and the World Cup boosted demand for ultra-high-definition TVs.

Drugmaker GSK slashes annual profits forecast

3 hours ago

British drugmaker GlaxoSmithKline on Wednesday slashed its 2014 profits forecast as second-quarter earnings sank on the back of weak US trade, adverse currency moves and a Chinese bribery probe.

Perthites wanted for study on the Aussie lingo

3 hours ago

We all know that Australians speak English differently from the way it's spoken in the UK or the US, and many of us are aware that Perth people have a slightly different version of the language from, say, Melbournians - but ...

User comments : 0