QuadriHunter - Catalog System for Quadratic Differential Systems

Step 1: Finite Singularities Count

Select the total number of real finite singular points present in the system:

Total Finite Singular Points:

Step 2: Characterize Finite Singularities

Distribute the stable elemental and semi-elemental configurations for the finite region:

Saddles (s) [Multiplicity 1 | Index -1]: Nodes / Foci / Antisaddles (a) [Multiplicity 1 | Index +1]: Centers (c) [Multiplicity 1 | Index +1]: Show multiple / higher-multiplicity finite configurations?

Step 3: Infinite Boundary Topology

How many pairs of infinite singular points are there?

Characterize the Infinite Pairs:

Saddle Pairs (Multiplicity 1 | Index: -1): Node Pairs (Multiplicity 1 | Index: +1): Saddle-Node Pairs (0,2) (Multiplicity 2 | Index: 0):

Saddle-Node Pairs (1,1) (Multiplicity 2 | Index: 0): Degenerate Pairs (1,2) [HHH-H] (Multiplicity 3 | Index: -1): Degenerate Pairs (1,2) [PHP-E] (Multiplicity 3 | Index: +1): Degenerate Pairs (1,2) [E-H] (Multiplicity 3 | Index: +1): Does the boundary have a higher degenerate pair (Multiplicity ≥ 4)?

Step 4: Limit Cycles Analysis (Bypassed)

The system prioritizes projective and boundary singularity classification.

Step 6: Topological Invariants Characterization

💡 Limit Cycles Coherence Rule: If your phase portrait contains nested limit cycles, please ignore their physical boundary and collapse all cycle nests toward their inner focus/antisaddle. Count any global separatrix arriving at the outer limit cycle as if it arrives directly to the interior finite singularity.

QuadriHunter Assistant

Step 1: Finite Singularities Count

Step 2: Characterize Finite Singularities

Step 3: Infinite Boundary Topology

Characterize the Infinite Pairs:

Step 4: Limit Cycles Analysis (Bypassed)

Step 6: Topological Invariants Characterization

📊 Finite Separatrices Count (I₂ Code Confection)

🌐 Infinite Separatrices Count (I₃ Code Confection)

Step 5: Final Classification Results