keep list pos.
[01] 2-Dimensional Linear Autonomous System of 1 Order 1. One of the eigenvalues is 0: 2. There are two eigenvalues with different signs: 3. There are two eigenvalues and both are positive 1: 4. There are two eigenvalues and both are positive 2: 5. There are two eigenvalues and both are negative: 6. The eigenvalues are double root, matrix A is diagonalizable: 7. The eigenvalues are double root, matrix A is not diagonalizable: 8. The eigenvalues are purely imaginary: 9. The eigenvalues have both real and imaginary parts: [02] 2-Dimensional Linear Autonomous System of 2 Order 1. Node-Saddle Point Type: 2. Degenerate Node-Saddle Point Type: 3. Double Elliptic Type: 4. Triple Crossing Type: 5. Node Type 2: 6. Parabolic Type: [03] High-order Simultaneous Autonomous System: 1. Homogeneous Autonomous System with periodic solution: 2. Homogeneous Autonomous System with eight parabolic sectors: 3. Homogeneous Autonomous System with compound sectors: 4. Vinograd's Autonomous System: [04] 2-Dimensional Autonomous System Examples: 1. Autonomous System with periodic equilibrium points on x-axis: 2. Autonomous System with 8 equilibrium points on the circumference: 3. Autonomous system with periodic equilibrium points on a plane: 4. Limit Cycle 1: 5. Limit Cycle 2: von del Pol: 6. Limit Cycle 3: Lemniscate: 7. Limit Cycle 4: for pure imaginary eigenvalues 1 8. Limit Cycle 5: for pure imaginary eigenvalues 2 9. Hamilton System 1: Cassini oval 10. Hamilton System 2: folium of Descartes 11. Hamilton System 3: derivatives of "folium of Descartes" 12. Hamilton System 4: for trigonometric functions [99] User defined Equations 0. User defined Equations 1. sample 1 2. sample 2 3. sample 3 4. sample 4 5. sample 5
Approximation method Euler's method Modified Euler's method 4th Order Runge-Kutta method
Equations
dx/dt=
dy/dt=
where, r=
dxdt=y dydt=sinx+y3
係数
a: e: b: f: c: g: d: h:
λ1,λ2= ±
Drawing Range -6.4 <x,y< 6.4
Step
Loop
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