| Multi-scale phenomenon exists in various forms in the process of biological growth, and it is the basic characteristic of the objective world. However, the effect of modulation by illumination on multiple-length-scale growth pattern formation and development has not been fully explained. In this paper, the copolymer gel was coupled with BZ reaction constructed a one-dimensional reaction-diffusion model in order to research the mechanism of reaction-diffusion dynamics and the law perturbation by illumination. The results showed that the evolution of progation distance of chemical waves during passage of time formed time-space pattern in multi-length scale. When the system is modulated by illumination with different intensity or forms, the multiple-length-scale pattern structure would occur with a serious of regular changes. The oscillatory frequency of BZ reaction plays an essential role in pattern structuring and chemical waves propagating.Firstly, the effect of light intensity on the oscillation frequency of the ruthenium catalyzed BZ reaction in the homogeneous system has been studied. The oscillation reaction can be induced or inhibited by illumination and a nonmonotonic relationship was found between oscillation frequency and illumination intensity, which the frequency increased firstly and then decreased. With the increasing of the concentration of Na Br O3 or HNO3, the range of light intensity that frequency increased by illumination decreased, which the effect of photoinhibition increased; with the increasing of the concentration of MA, the range of light intensity that frequency increased by illumination increased, which the effect of phoinduction increased.And then the effect of illumination on the spatio-temporal pattern has been studied. This paper found a nonmontonic relationship between oscillation frequency and illumination intensity in BZ gel system as the same as the homogeneous system. Chemical waves propagated with multiple-length-scale pattern structure. The complexity of the pattern structure increased with light intensity. The period on multiple-length-scale pattern changes from P4, P8, P16, P8, P4, P2 to P1 with increasing light intensiy. Further experiments were performed to investigate the effects of BZ reaction substrates(MA, Na Br O3, HNO3) on multiple-length-scale pattern structures perturbation by illumination and the phase diagrams showing the pattern structure of the system as function of light intensity and concentration of BZ substrates were obtained. When the concentration of Na Br O3 or HNO3 is in lower concentration range, the period decreased from P16, P8, P4, P2 to P1. When the concentration of Na Br O3 or HNO3 is in higher concentration range, which the system performed with higher oscillatory frequceny, the period on multiple-length-scale pattern performed the nonmontonic variation(P4→P8 →P16 → P8 → P4 → P2 → P1) beacause of the effect of photoinduction and photoinhibiton with increasing the light intensity. The effect of concentration of MA is different from Na Br O3 and HNO3. The system performed a nonmontonic relationship between oscillatory frequency and the concentration of MA. When the concentration of MA is in lower or higher concentration range, which the system performed with low oscillatory frequency, the period on pattern dereased with increasing light intensity: P16 → P8 → P4 → P2 → P1. And in the middle area of the concentration of MA, the period performed the nonmontonic variation: P4→P8 →P16 → P8 → P4 → P2 → P1.After that, the chemical waves modulated by period light in one-dimensional BZ gel open system. When the applied light intensity is periodically modulated, the system shows intermittern wave groups in the time-space plot or quasiperiodic oscillations in local dynamics and undulating wave groups in the time-space plots. The chemical wave groups change from intermittern-2(I2), I3, I4 I5, I6, I7, I8 to I9 as the illumination intensity increased from 400 s to 2800 s. When the period exceeds 3000 s, the wave pattern is quasiperiodic without intermittent groups. Further experiments were performed to investigate the phase diagram showing the behavior of the system as a function of forcing period and maximum light intensity. The phase diagram can be divided into five regions:(1) non-synchronization;(2) weak perturbation;(3) frequency-locked;(4) non-locked;(5) steady state.To explain the wave structure in this diffusion-fed gel system, finally, the modified Oregonator model were proposed to investgate photosensitive BZ mechanism to simulate the time-dependent light-perturbed reaction-diffusion waves. The simulated results were nearly quantitative agreement with the results and provided a reasonable explanation for the dynamical mechasim.In this paper, inspired the biological growth characteristics of photosynthesis, a reaction-diffusion system was constructed, which coupled the copolymer gel with BZ reaction, and studied the dynamical mechanism of multiple-length-scale pattern variation. Studying this growth structure may aid in understanding the influence of environmental variation on complex growth processes in living systems. |
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