摘要
在三模Lorenz方程的基础上,进一步研究四模Lorenz-Stenflo系统的动力学行为,讨论Lorenz-Stenflo方程解的性质和状态。求出该方程平衡点,计算其局部线性稳定性;利用Young不等式和Gronwall不等式讨论该方程组全局吸引子的存在性,构造李雅普诺夫函数对其全局稳定性进行分析;最后利用数值模拟方法,揭示了参数在一定范围内变化时四模Lorenz-Stenflo系统的动力学行为。人们对非线性现象的本质认识有限,所以通过数值模拟,能更加生动形象地描述出Lorenz-Stenflo吸引子的形状,进而让人们对该模型的混沌现象有更直观清晰的认识。参数的变化也导致了系统动力学行为的变化,在Lorenz系统加入气流旋转因素后,系统的动力学行为更加丰富。
Based on the three-dimensional Lorenz equation,we further study the dynamical behavior of the four-dimensional Lorenz-Stenflo system and discuss the properties and states of the solution of the Lorenz-Stenflo equation.The equilibrium point of the equation is obtained and its local linear stability is calculated;Using Young inequality and Gronwall inequality,the existence of the global attractor of the equations is discussed,and the Lyapunov function is constructed to analyze its global stability;Finally,using the numerical simulation method,the dynamic behavior of four-dimensional Lorenz-Stenflo system is intuitively displayed when the parameters change in a certain range.People have limited understanding of the essence of nonlinear phenomena,so through numerical simulation,we can more vividly describe the shape of Lorenz-Stenflo attractor,and then let people have a more intuitive and clear understanding of the chaotic phenomenon of the model.The change of parameters also leads to the change of chaotic behavior of the system.After the air flow rotation factor is added to the Lorenz system,the dynamic behavior of the system is richer.
作者
王贺元
白晨
WANG Heyuan;BAI Chen(College of Mathematics and Systems Science,Shenyang Normal University,Shenyang 110034,China)
出处
《沈阳师范大学学报（自然科学版）》
CAS
2022年第5期421-425,共5页
Journal of Shenyang Normal University:Natural Science Edition
基金
国家自然科学基金资助项目(11572146)。
