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Copyright CRC Press 2023 - present CRC Press

Author: Dr Stephen Lynch National Teaching Fellow FIMA SFHEA

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Chapter 16: Brain Inspired Computing

Chapter 17: Neural Networks and Neurodynamics

Question 17.4: Plotting bifurcation diagrams and comparing the results with the stability diagram in Figure 17.7(b). The eigenvalues are used to determine the stability boundaries.

The two-neuron module is modeled using the discrete system:

$$x_{n+1}=b_1+w_{11}\tanh(\alpha x_n)+w_{12}\tanh(\beta y_n), \\ y_{n+1}=b_2+w_{21} \tanh(\alpha x_n),$$

where $x_n, y_n$ are neuron activation potentials, $b_1, b_2$ are biases, $w_{11}$, $w_{12}$, and $w_{21}$ are synaptic weights.

There is a large bistable region for $-1 < b_1 < 2$, approximately. The solutions are in steady-state. Compare with the stability diagram in Figure 17.7(b).