Investigation of Chaotic Behaviors of Fractional Order Love Model Without External Environment Effect

In this paper, we focus on the nonlinear dynamic behavior of fractional order love model because the fractional order can reflect the 'memory dependency' of certain dynamic processes to a certain extent. The novel fractional order love model without external environment effect investigates two aspects: first, the chaotic dynamic of the used system when the system order is 2, and second, the smallest system order of fractional order love model that can generate chaotic behaviors. The simulation results show the fractional order love model can produce different results compared to the integer order model. While the fractional order love model still has chaotic behavior even the sum of the system order is equal to 2. Moreover, the smallest system order of fractional order love model having chaotic behavior is 1.7. The results indicate that two individuals can display love status even if the sum of the system order is less than 2 because the 'memory dependency' effects can greatly affect the emotional changes of human beings. The simulation results based on time series, phase portrait, power spectrum, Poincare map, maximal Lyapunov exponent and bifurcation diagram, and the conclusion is applied to the real life are also discussed.