The Study Of Transitions, Coherence And Spike Death Induced By Bounded Noise And Time Delays

The effects of bounded noise and time delays on both a model of tumor-immune system and an excitable system are studied in this thesis. First, the research status of the noise-induced motion, the necessity for the introduction of bounded noise, the models of tumor-immune system interplay and the features of excitable system are summarized. Then, after a detailed theoretical analysis, a possible definition of the cross-correlated sine-Wiener noises (as one type of bounded noise) and related simulation algorithm are given. Finally, the effects of bounded noise and time delays on both a model of tumor-immune system and an excitable system are investigated, and some results are as follows:A model of tumor-immune system interplay with time delays and cros correlated sine-Wiener noises is investigated by numerical simulations for the sta-tionary probability distribution (SPD) and stationary mean value〈χ〉st of tumor cell population. Results show that (i) the structure of the SPD transfers from bimodal to unimodal as the reaction time (τα) of the cell population to environ-mental constraints increases;(ii) conversely, as the time (τβ) of immune system to develop specific immune competence and the correlation time (τ) of noises in-crease, the structure of the SPD transfers from the unimodality to the bimodality;(iii) as the cross-correlated intensity (λ’) between noises increases, the transitions induced by τ are suppressed. The transitions show that the perturbations and delays contribute to triggering the immune degradation or tumor growth cease. Our results may be helpful for elucidating basic mechanisms of the formation of tumor.The FitzHugh-Nagumo model with sine-Wiener noise and delayed feedback is numerically investigated. A minimum of the coefficient of variation (R) of interspike intervals is observed both as a function of the noise intensity and as a function of the noise correlation time, viz, the coherence resonance phenomenon. Also, in the scenario of purely noise-sustained irregular oscillations, there exists a maximum of R as a function of the delay time (Td) of feedback, namely, the suppressed coherence. Moreover, in the scenario of purely noise-sustained regular oscillations, the R with multiple peaks as a function of of can be observed, that is, the oscillatory coherence. Additionally, within the tailored parameter regime, spike death phenomenon can be obtained. These results may be helpful for making artificial devices.Finally, from the above, we find that the combination of delay and noise can substantially modulate the dynamic behavior of systems.