Phasing into PHASER

نویسنده

  • JAMES T. TOWNSEND
چکیده

The guts of this package consist of the software contained in the diskette that accompanies the text. However, the text is necessary until one becomes familiar with the operations. A subtitle expands as follows: With a Supplementary Diskette Containing PHASER: An Animator/ Simulator for Dynamical Systems for IBM Personal Computers. This tells the potential reader and user basically what to expect. Without some qualifiers, that individual may be led to expect too much, but for the price, the package delivers a lot. Deterministic-that is, nonstochastic-dynamics are based on differential equations for modeling continuous time phenomena, whereas difference equations are employed to model discrete time data. PHASER was developed by Hiiseyin K~ak at Brown University to: (1) illustrate some of the most famous continuous and discrete dynamic systems through their difference or differential equations and (2) permit users to explore their own dynamic systems. An important aspect of (1) is that PHASER is designed to handle nonlinear dynamics. Linear dynamics admit well-known solutions, and in the event of time-invariant, linear systems, the solutions can usually be expressed in closed form. In any event, the theory is almost completely worked out and there are no real surprises. With nonlinear dynamics, the situation is quite the opposite: Very little of a general nature can be said about arbitrary classes of nonlinear differential equations and their systemic behavior. Indeed, in many such systems, chaotic behavior can occur (see, e.g., Devaney, 1986; Townsend, in press). Although mathematicians and other scientists have begun to learn much about the nature of nonlinear systems and such phenomena as chaos over the past few decades,

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تاریخ انتشار 2015