Nonlinear Dynamic Models in Advanced Life Support 2002-01-2291
To facilitate analysis, Advanced Life Support (ALS) systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. This paper reviews nonlinear models applicable to ALS. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Because most mathematical analysis applies to linearized systems, nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays can be a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode or overflow the buffer. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain the sums, differences, and harmonics of input frequencies. A nonlinear system may also produce unexpected time behavior, such as a stable limit cycle oscillation not driven by input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.