Semester project
![](https://private-user-images.githubusercontent.com/95555641/396349984-8d0c3eee-66f6-4f9d-9d02-463a6fae656f.png?jwt=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.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.WIyvBDMmYwegXjEPKnz6myVmCPPSL2-lnujVNlx2sl0)
![](https://private-user-images.githubusercontent.com/95555641/396509734-a28131c9-38be-403e-bb96-19e55f7f26d6.png?jwt=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.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.t0w1kYR5seUxzM4PX7RBBUZcxLSFTB5YMD1pVYvONvg)
![](https://private-user-images.githubusercontent.com/95555641/396361242-c686f217-f56e-412f-a843-ea1785c08f48.png?jwt=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.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.E9dxMQjLzsoGG6r39TXHB16j4tuv1_dI1ix-W6Da3Fs)
Simulate depolarizing current pulses of various amplitudes by setting the voltage initial condition to a succession of values positive to the resting potential while starting w at the equilibrium point.
Action potentials are usually thought to have thresholds. Does the MLE with the given set of parameters have a threshold depolarization?
![](https://private-user-images.githubusercontent.com/95555641/396507461-630c52a0-6b0d-460e-ac1c-8c3781aa1d9f.png?jwt=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.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.f40L4SzXH1nc_izGAZH3mL9rOoMyXPTItAIib_6nygM)
Plot of phase-plane trajectories for values of initial depolarization that do and do not produce action potentials.
![](https://private-user-images.githubusercontent.com/95555641/396507768-0c5865b2-95ea-472a-88e3-6e3117b9b0e3.png?jwt=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.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.awvNkgiEQK19UL7Ag0EARGJ77_HaWOwAHqQ7u8Ij5bY)
- Set the initial conditions to the equilibrium point used above, appropriate for Iext=0;
- Set the initial conditions to the equilibrium point when Iext=86 μA/cm2;
- Set the initial conditions off the equilibrium point for Iext=86 μA/cm2, say at (-27.9, 0.17).
![](https://private-user-images.githubusercontent.com/95555641/396544357-1dff8290-424a-4b9f-8583-01b03332b554.png?jwt=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.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.CdbHadpa00imQKtvDiJ0P4yF7pVhU57AGKm35qSZfkQ)