[1] has proved that the dissipative Zakharov system has an ε2-weak compact attractor. In this paper, we further show that the dissipative Langmuir waves in plasmas admit an inertial fractal set of (ε2,ε1)-type. We ...[1] has proved that the dissipative Zakharov system has an ε2-weak compact attractor. In this paper, we further show that the dissipative Langmuir waves in plasmas admit an inertial fractal set of (ε2,ε1)-type. We also make the estimates on its fractal dimension and exponential attraction.展开更多
Many questions in natural science and engineering can be transformed into nonlinear equations. Newton iteration method is an important technique to one dimensional and multidimensional variables and iteration itself i...Many questions in natural science and engineering can be transformed into nonlinear equations. Newton iteration method is an important technique to one dimensional and multidimensional variables and iteration itself is very sensitive to initial guess point. This sensitive area is the Julia set of nonlinear discrete dynamic system which Newton iteration method forms. The Julia set, which is the boundaries of basins of attractions, displays the intricate fractal structures and chaos phenomena. By constructing repulsion two-cycle point function and making use of inverse image iteration method, a method to find Julia set point was introduced. For the first time, a new method to find all solutions was proposed based on utilizing sensitive fractal areas to locate the Julia set points to find all solutions of the nonlinear questions. The developed technique used an important feature of fractals to preserve shape of basins of attraction on infinitely small scales. The numerical examples in linkage synthesis showed that the method was effective and correct.展开更多
文摘[1] has proved that the dissipative Zakharov system has an ε2-weak compact attractor. In this paper, we further show that the dissipative Langmuir waves in plasmas admit an inertial fractal set of (ε2,ε1)-type. We also make the estimates on its fractal dimension and exponential attraction.
基金Sponsored by the Scientific Research Fund of Ministry Education(Grant No.02108),and the Key Scientific Research Fund of Hunan Provincial Education Depart-ment(Grant No.04A036),and the Grant of the11-th Five-year Plan for Key Construction Disciplines Mechanical Design and Theory of Hunan Province.
文摘Many questions in natural science and engineering can be transformed into nonlinear equations. Newton iteration method is an important technique to one dimensional and multidimensional variables and iteration itself is very sensitive to initial guess point. This sensitive area is the Julia set of nonlinear discrete dynamic system which Newton iteration method forms. The Julia set, which is the boundaries of basins of attractions, displays the intricate fractal structures and chaos phenomena. By constructing repulsion two-cycle point function and making use of inverse image iteration method, a method to find Julia set point was introduced. For the first time, a new method to find all solutions was proposed based on utilizing sensitive fractal areas to locate the Julia set points to find all solutions of the nonlinear questions. The developed technique used an important feature of fractals to preserve shape of basins of attraction on infinitely small scales. The numerical examples in linkage synthesis showed that the method was effective and correct.
