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This Concept Map, created with IHMC CmapTools, has information related to: a1. Basic Dynamical Systems Overview, These systems are either ???? Non-Equlibrium Open Systems:, Linear Systems versus Non-Linear Systems, As Systems Progress they fall on an ???? b1Attractor, Future Values predictable only in the short range ???? These systems are either, Closed Systems: In Equibrium progress to Non-Equlibrium Open Systems:, Non-Linear Systems diverge over time Perturbations to Non-Linear systems Small Perturbations May Result in Large Changes in System Trajectory, Linear Systems ???? Linear Systems remain regular over time, they Progresses in lock step, Dynamical Systems are Systems which CHANGE or evolve over TIME or they can be Non-Linear Systems, The logistic equation; a simple equation or formula for approximating evolution over time. ???? c4. Logistic Equation, Progresses Farther and Farther from Equilibrium. System. becomers Erratic, Long-Term Predictions become Impossible ???? As Systems Progress they fall on an, Dynamical Systems are Systems which CHANGE or evolve over TIME they can be Linear Systems, Linear Systems remain regular over time, they Progresses in lock step perturbations to Linear systems Die Out, Linear Systems remain regular over time, they Progresses in lock step ???? Future Values are Predictable, a1. Dynamical Systems Overview ???? Dynamical Systems are Systems which CHANGE or evolve over TIME, Non-Linear Systems diverge over time plot The logistic equation; a simple equation or formula for approximating evolution over time., Non-Equlibrium Open Systems: System exchanges energy, matter and information with surroundings allowing it to Progresses Farther and Farther from Equilibrium. System. becomers Erratic, Long-Term Predictions become Impossible, Future Values are Predictable ???? Invariant to Time Reversal., Future Values predictable only in the short range ???? When parameter k ranges between 0 and 3, Closed Systems: In Equibrium Early in progression Future Values are Predictable, Progresses Farther and Farther from Equilibrium. System. becomers Erratic, Long-Term Predictions become Impossible leading to Chaos a15. Routs to Chaos