Analysis and Simulation of Chaotic Systems 2nd ed. - F. Hoppensteadt
This book describes aspects of mathematical modeling, analysis, computer
simulation, and visualization that are widely used in the mathematical
sciences and engineering.
Scientists often use ordinary language models to describe observations
of physical and biological phenomena. These are precise where data are
known and appropriately imprecise otherwise. Ordinary language modelers
carve away chunks of the unknown as they collect more data. On the other
hand, mathematical modelers formulate minimal models that produce re-sults similar to what is observed. This is the Ockham’s razor approach,
where simpler is better, with the caution from Einstein that “Everything
should be made as simple as possible, but not simpler.”
The success of mathematical models is diļ¬cult to explain. The same
tractable mathematical model describes such diverse phenomena as when
an epidemic will occur in a population or when chemical reactants will
begin an explosive chain-branched reaction, and another model describes
the motion of pendulums, the dynamics of cryogenic electronic devices, and
the dynamics of muscle contractions during childbirth.
Ordinary language models are necessary for the accumulation of experi-mental knowledge, and mathematical models organize this information, test logical consistency, predict numerical outcomes, and identify mechanisms and parameters that characterize them.
- Publisher: Springer; 2nd edition (January 21, 2000)
- Language: English
- ISBN-10: 0387989439
- ISBN-13: 978-0387989433
This book describes aspects of mathematical modeling, analysis, computer
simulation, and visualization that are widely used in the mathematical
sciences and engineering.
Scientists often use ordinary language models to describe observations
of physical and biological phenomena. These are precise where data are
known and appropriately imprecise otherwise. Ordinary language modelers
carve away chunks of the unknown as they collect more data. On the other
hand, mathematical modelers formulate minimal models that produce re-sults similar to what is observed. This is the Ockham’s razor approach,
where simpler is better, with the caution from Einstein that “Everything
should be made as simple as possible, but not simpler.”
The success of mathematical models is diļ¬cult to explain. The same
tractable mathematical model describes such diverse phenomena as when
an epidemic will occur in a population or when chemical reactants will
begin an explosive chain-branched reaction, and another model describes
the motion of pendulums, the dynamics of cryogenic electronic devices, and
the dynamics of muscle contractions during childbirth.
Ordinary language models are necessary for the accumulation of experi-mental knowledge, and mathematical models organize this information, test logical consistency, predict numerical outcomes, and identify mechanisms and parameters that characterize them.
