Bme 6938 neurodynamics
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BME 6938 Neurodynamics. Instructor: Dr Sachin S Talathi. Phase of limit cycle. Isochrons-Define phase off limit cycle. Phase of a non periodic point is taken to be the phase of its periodic proxy. Phase Response Curve. Weak Coupling- Infinitesimal PRC. Linear Response Function or iPRC.

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BME 6938 Neurodynamics

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BME 6938Neurodynamics

Instructor: Dr Sachin S Talathi

Phase of limit cycle

Isochrons-Define phase off limit cycle

Phase of a non periodic point is taken to be the phase of its periodic proxy

Phase Response Curve

Weak Coupling- Infinitesimal PRC

Linear Response Function or iPRC

Practical Approach to Calculating iPRC

  • Malkin’s Theorem:

    Let the system have exponentially stable limit cycle with period T and receive infinitesimal periodic perturbation

    Then its phase is described by equation

    Where with

    (XPPAUTO exploits this theorem to estimate iPRC)

Brain rhythms (EEG) correlate with behavioral states

  • Delta (0.5-4 Hz):

  • Dominant rhythm in infants and stage 3 and 4 of sleep

  • Theta (4-8 Hz):

  • Normal activity in young children and represents drowsiness in adults

  • Alpha (8-12 Hz):

  • It is observed in relaxed state

  • Beta (12-30 Hz):

  • Observed in an anxious state

  • Gamma (>30 Hz):

  • Observed in attention state and is thought to be the learning rhythm




Deep Sleep

Neural synchrony: Mechanism for generation of brain rhythms

Synchronous activity is large-detectable at the electrodes on the scalp (source of EEG)

Neural Synchrony and the Binding Problem

  • No central location in the brain where all information related to a task is centralized

  • How are the parallel computations in spatially segregated regions in the brain coordinated?

  • How are signals selected and routed from sensory structures to executive structures without confounding?

  • How information about relatedness of content is encoded?

  • Related to the problem of consciousness

  • Potential Answer: Neural synchrony

How does synchrony arise?

Two key mechanisms.

  • Related to the intrinsic properties of neurons in terms their preference for input frequencies (resonance)

  • Related to the pattern of connectivity between neurons and the dynamic properties of intervening synapses (network and network interactions)

Note: These are not mutually exclusive explanations

Weakly coupled oscillators




Two weakly coupled oscillators

represents deviation from the identical period for each oscillator

Analyze Simple network-Weak Coupled Oscillators

Phase Locked Solution:

Stability Criteria:

Results from Weak Coupling Theory Analysis

Spike Time Response Curves

Coupling parameters

perturbation time

Intrinsic period

Analysis of the network using STRCs

Phase Locked Solution:

Stability Criterion:

Results from analysis using STRCs

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