Outline Models’ equations Some mathematical properties.

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Presentation transcript:

Outline Models’ equations Some mathematical properties. Classification of equilibrium points About limit cycles and saddle loop Phase portraits. Summary

Models’ equations:

Mathematical analysis Nullclines:

Mathematical analysis Number of equilibrium points

Mathematical analysis Divergence curve Theorem :the divergence curve has exactly one minimum and one maximum point.

Mathematical analysis

Mathematical analysis I-V relation

Invariant sets

Invariant sets ( equilibriums)

Invariant sets ( limit cycle)

Invariant sets ( Homoclinic loop)

Phase portraits

Phase portraits in absence of A and B

Phase portraits with one segment

Phase portraits with two segment

Phase portraits with two segment

Phase portraits with two segment

Phase portraits with two segment

Phase portraits with two segment

Phase portraits with two segment

Summary(ML Model with one segment)

Summary(ML Model with two segment)

Tanks for your attention