![]() ![]() They consist of a plot of typical trajectories in the state space. Set of initial conditions is represented by a different curve, or point. ![]() However, an attractor becomes a repeller when you consider t → −∞ and vice versa. Not invertible), we are mostly interested in understanding the behavior of solutions when t → ∞. Since the independent variable t is associated with time (which in reality is Remember that solutions to constant coefficient linear system of differential equations exist for all t ∈ (−∞, ∞). Alternatively, if trajectories near a stationary point leave it as t → ∞, then the critical point is referred to as the repeller or source. Since the general treatment of stability and instability is given in Part III of this tutorial, it is reasonable to provide its descriptive definition.Ī critical point is called an attractor or sink if every solution in a proximity of it moves toward to the stationary point (so it converges to the critical We will classify the critical points of various systems of first order linear differential equations by their stability. How the solutions of a given system of differential equations would behave in a neighborhood of the critical point. \) Similar to a direction field for a single differential equation, a phase portrait is a graphical tool to visualize Introduction to Linear Algebra with Mathematica Glossary Return to the main page for the second course APMA0340 ![]() Return to the main page for the first course APMA0330 Return to Mathematica tutorial for the second course APMA0340 Return to Mathematica tutorial for the first course APMA0330 Return to computing page for the second course APMA0340 Return to computing page for the first course APMA0330 Laplace equation in spherical coordinates.Numerical solutions of Laplace equation.Laplace equation in infinite semi-stripe.Boundary Value Problems for heat equation.Part VI: Partial Differential Equations.Part III: Non-linear Systems of Ordinary Differential Equations.Part II: Linear Systems of Ordinary Differential Equations. ![]()
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