LIFESCI 30B Lecture Notes - Lecture 23: Exclusive Or, Equilibrium Point, Exponential Growth
Document Summary
Time dynamical systems : ( fta" ]=f as. yeathy. 14<1 then exponential growth . ( tf r is negative then then exp . decay oscillation occurs. Behavior is completely determined by eigenvalues ( and eigenvector ) red : 1 1>1 then exponential growth along eigenvector line . of. 1 1<1 , then exponential decay along eigenvector line. X< 0 then oscillation w/ exp . growth / decay. Then oscillations rotations combined w/ exp . growth / decay. 1 1>1 then rotation exp . growth ( spiral outward ) unstable. Note point @ origin) inward ) eq . neutral stable ) X=atbi iii. i the a z . complex conjugate of. Then then exp . growth exp . decay. Behavior is completely determined by eigenvalues ( and eigenvectors ) of m. Then exp . growth + rotations ( spiral outward unstable then exp . decay rotations ( spiral inward stable then just rotation.
