In this paper, the impacts of the recycled signal on the dynamic complexity have been studied theoretically and numerically in a prototypical nonlinear dynamical system. The Melnikov theory is employed to determine the critical boundary, and the statistical complexity measure(SCM) is defined and calculated to quantify the dynamic complexity. It has been found that one can switch the dynamics from the periodic motion to a chaotic one or suppress the chaotic behavior to a periodic one, merely via adjusting the time delay or the amplitude of the recycled signal, therefore, providing a candidate to tame the dynamic complexity in nonlinear dynamical systems.
The combined effects of Lvy noise and immune delay on the extinction behavior in a tumor growth model are explored. The extinction probability of tumor with certain density is measured by exit probability. The expression of the exit probability is obtained using the Taylor expansion and the infinitesimal generator theory. Based on numerical calculations, it is found that the immune delay facilitates tumor extinction when the stability index α < 1, but inhibits tumor extinction when the stability index α > 1. Moreover, larger stability index and smaller noise intensity are in favor of the extinction for tumor with low density. While for tumor with high density, the stability index and the noise intensity should be reduced to promote tumor extinction.
This paper mainly investigates dynamics behavior of HIV(human immunodeficiency virus) infectious disease model with switching parameters, and combined bounded noise and Gaussian white noise. This model is different from existing HIV models. Based on stochastic It o lemma and Razumikhin-type approach, some threshold conditions are established to guarantee the disease eradication or persistence. Results show that the smaller amplitude of bounded noise and ˉR0< 1can cause the disease to die out; the disease becomes persistent if R0> 1. Moreover, it is found that larger noise intensity suppresses the prevalence of the disease even if R0> 1. Some numerical examples are given to verify the obtained results.
