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Discrete Dynamical Systems

2013
This short chapter presents the mathematics of matrix population models. The first section examines discrete linear systems using scalar notation and computer simulations. The simulations lead to the discovery of an asymptotic growth rate and stage structure, which we can determine by ad hoc methods for systems of only two or three components.
Morris W. Hirsch   +2 more
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Discrete Dynamical Systems

1998
A discrete dynamical system is a system which is discrete in time so we observe its dynamics not continuously but at the given moments of time like in the case of Poincare maps introduced in the previous chapter. The dynamics of discrete dynamical systems is usually simple enough to be explained in details.
Yushu Chen, Andrew Y. T. Leung
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Discrete Dynamical Systems

2000
In this chapter we will study sequences defined by recurrence relations of the form x n+1 = f (x n ). This is a topic which has an interesting history and which has seen rapid development in recent years. Its study requires little in the way of mathematical preparation, and there are even interesting applications.
George C. D, Jean Michel F, Henri L
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MEMORY EFFECTS IN DISCRETE DYNAMICAL SYSTEMS

International Journal of Bifurcation and Chaos, 1992
Let fµ(s)=µs(1−s) be the family of logistic maps with parameter µ, 1≤µ≤4. We present a study of the second-order difference equation xn+1=fµ([1−∈]xn+∈xn−1), 0≤∈≤1, which reduces to the well-known logistic equation as ∈=0.
INVERNIZZI, SERGIO, Aicardi F.
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Discrete Dynamical Systems

2009
Suppose we wish to describe some physical system. The dynamical systems approach considers the space X of all possible states of the system—think of a point x in X as representing physical data. We will assume that X is a subset of some normed vector space, often \({\mathbb{R}}\).
Kenneth R. Davidson, Allan P. Donsig
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Discrete Dynamical Systems

2015
So far we have discussed the dynamics of continuous systems. An evolutionary process may also be expressed mathematically as discrete steps in time. Discrete systems are described by maps (difference equations). The composition of map generates the dynamics or flow of a discrete system.
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Discrete Dynamic Systems

2016
This chapter introduces discrete dynamic systems by first looking at models for dynamic and static aspects of systems, before covering continuous and discrete systems.
Matthias Kunze, Mathias Weske
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