Bifurcation Diagrams, Phase Portraits, and Neuron Simulation: A Neural Networks Project - , Study Guides, Projects, Research of Electrical and Electronics Engineering

Download Bifurcation Diagrams, Phase Portraits, and Neuron Simulation: A Neural Networks Project - and more Study Guides, Projects, Research Electrical and Electronics Engineering in PDF only on Docsity! Bifurcation Diagrams, Phase Portraits, and Neuron Simulation version 12 May 2009 ECE 6730 Artificial [Advanced] Neural Networks Recall that you may not use any references in completing this project without permission from the course instructor. Carefully document your work using the homework format described in the syllabus. A formal report is not required. 1. Consider the discrete-time dynamical system (“logistic map”) where [1] [ 1] [ ](1 [ ])x k x k x kλ+ = − Using MATLAB®, provide a bifurcation diagram for this system as discussed in class where λ>0 is the bifurcation parameter. Provide plots of the state x vs. step k for “interesting” regions of the bifurcation diagram. 2. Consider a parallel RLC circuit with an initial capacitor voltage. Derive a state space description of this continuous-time dynamical system. Consider the value of R (which can be positive or negative) to be a bifurcation parameter. Provide several phase portraits and the corresponding time domain plots for this system for different values of R. You may use LTspice IV (http://www.linear.com/) and/or MATLAB®. 3. Install the NEURON simulation environment available at http://neuron.duke.edu/ . Complete the first three tutorials available at http://www.kem.org/neuron/tutorial.html. Investigate the effects of different stimulation current levels in tutorial #1 to include generation of a “typical” action potential. References [1] E. Ott, Chaos in Dynamical Systems, Cambridge University Press, 1993. © 2009 Damon A. Miller. All rights reserved.