Answered: Refer to page 3 for stability in… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.7: The Inverse Of A Matrix

Problem 30E

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Refer to page 3 for stability in differential systems.
Instructions:
1.
2.
Analyze the phase plane of the system provided in the link to determine stability.
Discuss the role of Lyapunov functions in proving stability.
3.
Evaluate the impact of eigenvalues of the Jacobian matrix on the nature of equilibria.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]

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The Different Effects of Excitation and Inhibition in Neural Circuit (series #1)| Neural circuit consists of polysynaptic neural network, combination of excitatory and inhibitory neurons. This exercise helps to understand the effects of excitation and inhibition in the nervous system. Our body is dynamically active under physiology condition. As a result, there are basal levels of activity such as 70 beats/min of heart rate at resting condition. Either increased or decreased activities are relative to the baseline. The effects of excitation are easily understood---one neuron activates another neuron. However, when inhibition is introduced into circuits, analysis become more complicated. In fact, the numbers of inhibitory neurons in the circuit determine the final effect of the circuit, which can be excitation or inhibition, on the target organ or area. We assume all excitatory and inhibitory neurons are glutamate and GABA neurons, respectively, in this practice sheet. The glutamate and…
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determine the eigenvalues and eigenvectors if the eigenvalues are real (or use results from exercises from Section 4.2. if you have covered those exercises). Also classify the system (state whether stable or unstable node, stable or unstable spiral, center, saddle point) and in all cases sketch the phase plane of the linear system. (As a hint, problems with * have complex eigenvalues.) When checking your answers with those in the back of the book, keep in mind that any nonzero multiple of the given eigenvector may be used.

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