ABSTRACT
ABSTRACT: In this work, nonlinear vibration of a happiness model with commensurate fractional-order derivative is studied analytically and ascertained by numerical ones. The influences of the impact factor of memory on the curves of external frequency, excitation amplitude, and nonlinear damping coefficient versus maximal amplitude of one’s response to external events are presented and compared by introducing the polynomial homotopy continuation technique. The result shows that when one’s experiences have more and more influences on his/her present and future life, the vibration amplitude of one’s response to external events becomes bigger and bigger under the same external events, and some strong nonlinear phenomena such as multiple solutions, bifurcation and peak amplitude with the increasing impact factor of memory are illustrated. In addition, we can find that all the stable solution branches obtained match well with the numerical ones.
