Local Dynamics of a New Four-Dimensional Quadratic Autonomous System  

作　　者：Sengen Hu Liangqiang Zhou Sengen Hu;Liangqiang Zhou(School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China;Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA), Nanjing, China)

机构地区：[1]School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China [2]Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA), Nanjing, China

出　　处：《Journal of Applied Mathematics and Physics》2022年第9期2632-2648,共17页应用数学与应用物理（英文）

摘　　要：In this manuscript, Local dynamic behaviors including stability and Hopf bifurcation of a new four-dimensional quadratic autonomous system are studied both analytically and numerically. Determining conditions of equilibrium points on different parameters are derived. Next, the stability conditions are investigated by using Routh-Hurwitz criterion and bifurcation conditions are investigated by using Hopf bifurcation theory, respectively. It is found that Hopf bifurcation on the initial point is supercritical in this four-dimensional autonomous system. The theoretical results are verified by numerical simulation. Besides, the new four-dimensional autonomous system under the parametric conditions of hyperchaos is studied in detail. It is also found that the system can enter hyperchaos, first through Hopf bifurcation and then through periodic bifurcation.In this manuscript, Local dynamic behaviors including stability and Hopf bifurcation of a new four-dimensional quadratic autonomous system are studied both analytically and numerically. Determining conditions of equilibrium points on different parameters are derived. Next, the stability conditions are investigated by using Routh-Hurwitz criterion and bifurcation conditions are investigated by using Hopf bifurcation theory, respectively. It is found that Hopf bifurcation on the initial point is supercritical in this four-dimensional autonomous system. The theoretical results are verified by numerical simulation. Besides, the new four-dimensional autonomous system under the parametric conditions of hyperchaos is studied in detail. It is also found that the system can enter hyperchaos, first through Hopf bifurcation and then through periodic bifurcation.

关 键 词：Four-Dimensional Autonomous System Routh-Hurwitz Criterion Hopf Bifurcation HYPERCHAOS 

分 类 号：O41[理学—理论物理]