Examining phototactic bioconvection in non-scattering suspensions with upper heating and collimated irradiation, this study delves into the intricate dynamics influenced by light and microorganisms. The study focuses on the linear stability of the basic state, examining neutral curves. The numerical analysis involves solving a system of equations using the MATLAB bvp4c solver. The investigation considers the impact of parameters, such as the thermal Rayleigh number, critical total intensity, and Lewis number, on the critical bioconvection Rayleigh number. As the critical total intensity varies, a transition from a stationary to an oscillatory solution (and vice versa) is observed. Phototactic microorganisms are incorporated into the model, and the results show how varying parameters affect convection patterns and stability. The findings reveal interesting phenomena, including Hopf bifurcations and limit cycles.

中文翻译：

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在非散射悬浮液中从上方加热：准直照射下的趋光生物对流

这项研究通过上部加热和准直照射检查非散射悬浮液中的趋光生物对流，深入研究了光和微生物影响的复杂动力学。该研究的重点是基本状态的线性稳定性，检查中性曲线。数值分析涉及使用 MATLAB bvp4c 求解器求解方程组。研究考虑了热瑞利数、临界总强度和路易斯数等参数对临界生物对流瑞利数的影响。随着临界总强度的变化，可以观察到从静止溶液到振荡溶液的转变（反之亦然）。趋光微生物被纳入模型中，结果显示不同的参数如何影响对流模式和稳定性。研究结果揭示了有趣的现象，包括 Hopf 分岔和极限环。