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ON A PROBLEM IN COMPLEX OSCILLATION THEORY OF PERIODIC HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS
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作者 肖丽鹂 陈宗煊 《Acta Mathematica Scientia》 SCIE CSCD 2010年第4期1291-1300,共10页
In this article, the zeros of solutions of differential equation f^(k)(z)+A(z)f(z) = 0, are studied, where k 2, A(z) = B(e^z), B(ζ) = g1(1/ζ) + g2(ζ), g1 and g2 being entire functions with g2 tr... In this article, the zeros of solutions of differential equation f^(k)(z)+A(z)f(z) = 0, are studied, where k 2, A(z) = B(e^z), B(ζ) = g1(1/ζ) + g2(ζ), g1 and g2 being entire functions with g2 transcendental and σ(g2) not equal to a positive integer or infinity. It is shown that any linearly independent solutions f1, f2, . . . , fk of Eq.(*) satisfy λe(f1 . . . fk) ≥ σ(g2) under the condition that fj(z) and fj(z+ 2πi) (j = 1, . . . , k) are linearly dependent. 展开更多
关键词 Differential equation PERIODIC linearly dependent complex oscillation
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ZEROS OF ENTIRE SOLUTIONS TO COMPLEX LINEAR DIFFERENCE EQUATIONS 被引量:7
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作者 陈宗煊 《Acta Mathematica Scientia》 SCIE CSCD 2012年第3期1141-1148,共8页
In this article, we study the complex oscillation problems of entire solutions to homogeneous and nonhomogeneous linear difference equations, and obtain some relations of the exponent of convergence of zeros and the o... In this article, we study the complex oscillation problems of entire solutions to homogeneous and nonhomogeneous linear difference equations, and obtain some relations of the exponent of convergence of zeros and the order of growth of entire solutions to complex linear difference equations. 展开更多
关键词 Linear difference equation complex oscillation ZERO order of growth
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Internal motion of the complex oscillators near main resonance
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作者 Jan Awrejcewicz Roman Starosta 《Theoretical & Applied Mechanics Letters》 CAS 2012年第4期19-22,共4页
An analytical study of the two degrees of freedom nonlinear dynamical system is presented. The internal motion of the system is separated and described by one fourth order differential equation. An approximate approac... An analytical study of the two degrees of freedom nonlinear dynamical system is presented. The internal motion of the system is separated and described by one fourth order differential equation. An approximate approach allows reducing the problem to the Duffing equation with adequate initial conditions. A novel idea for an effective study of nonlinear dynamical systems consisting in a concept of the socalled limiting phase trajectories is applied. Both qualitative and quantitative complex analyses have been performed. Important nonlinear dynamical transition type phenomena are detected are investigated analytically. 展开更多
关键词 nonlinear dynamics multiple scale method complex oscillator internal motion
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Synchronization of Spatiotemporal Chaos in Coupled Complex Ginzburg—Landau Oscillators
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作者 GAOjI-Hua ZHENGZhi-Gang JIANGLian-Bo 《Communications in Theoretical Physics》 SCIE CAS CSCD 2003年第4期429-432,共4页
Synchronization of spatiotemporal distributed system is investigated by considering the model of 1D dif-fusively coupled complex Ginzburg-Landau oscillators. An itinerant approach is suggested to randomly move turbule... Synchronization of spatiotemporal distributed system is investigated by considering the model of 1D dif-fusively coupled complex Ginzburg-Landau oscillators. An itinerant approach is suggested to randomly move turbulentsignal injections in the space of spatiotemporal chaos. Our numerical simulations show that perfect turbulence synchro-nization can be achieved with properly selected itinerant time and coupling intensity. 展开更多
关键词 spatiotemporal chaos chaos synchronization coupled complex Ginzburg-Landau oscillators
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A NOTE ON THE COMPLEX OSCILLATION FOR HIGHER ORDER HOMOGENEOUS LINEAR DIFFERENTIAL EQUATIONS 被引量:2
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作者 高仕安 汤家凤 《Annals of Differential Equations》 1996年第2期167-172,共6页
In this paper, we are concerned with the maximum number of linearly independent transcendental solutions with finite exponent of convergence of the zeros for a higher order homogeneous linear differential equation whe... In this paper, we are concerned with the maximum number of linearly independent transcendental solutions with finite exponent of convergence of the zeros for a higher order homogeneous linear differential equation where its coefficients are entire functions with order less than 1/2 and one dominant. The result obtained here is an extension and a complement of J. K. Langley's. 展开更多
关键词 value distribution differential equation complex oscillation
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PERTURBATION RESULTS OF SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS WITH PERIODIC COEFFICIENTS
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作者 Huang Zhibo Chen Zongxuan 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2007年第4期405-412,共8页
Two perturbation results on the linear differential function f″ + Π(z)A(z)f = 0 are obtained, where Π(z) and A(z) are periodic entire functions with period 2πi and σe(Π) 〈 σe(A).
关键词 complex oscillation differential function PERIOD linearly dependent linearly independent.
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Analytical approximations to a generalized forced damped complex Duffing oscillator:multiple scales method and KBM approach 被引量:1
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作者 Weaam Alhejaili Alvaro H Salas S A El-Tantawy 《Communications in Theoretical Physics》 SCIE CAS CSCD 2023年第2期18-27,共10页
In this investigation,some different approaches are implemented for analyzing a generalized forced damped complex Duffing oscillator,including the hybrid homotopy perturbation method(H-HPM),which is sometimes called t... In this investigation,some different approaches are implemented for analyzing a generalized forced damped complex Duffing oscillator,including the hybrid homotopy perturbation method(H-HPM),which is sometimes called the Krylov-Bogoliubov-Mitropolsky(KBM)method and the multiple scales method(MSM).All mentioned methods are applied to obtain some accurate and stable approximations to the proposed problem without decoupling the original problem.All obtained approximations are discussed graphically using different numerical values to the relevant parameters.Moreover,all obtained approximate solutions are compared with the 4thorder Runge-Kutta(RK4)numerical approximation.The maximum residual distance error(MRDE)is also estimated,in order to verify the high accuracy of the obtained analytic approximations. 展开更多
关键词 complex Duffing oscillators forced damped complex oscillator multiple scales method KBM method
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On precise time integration method for non-classically damped MDOF systems
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作者 汪梦甫 周锡元 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2006年第1期79-85,共7页
In the complex mode superposition method, the equations of motion for non-classically damped multiple-degree-of-freedom (MDOF) discrete systems can be transferred into a combination of some generalized SDOF complex ... In the complex mode superposition method, the equations of motion for non-classically damped multiple-degree-of-freedom (MDOF) discrete systems can be transferred into a combination of some generalized SDOF complex oscillators. Based on the state space theory, a precise recurrence relationship for these complex oscillators is set up; then a delicate general solution of non-classically damped MDOF systems, completely in real value form, is presented in this paper. In the proposed method, no calculation of the matrix exponential function is needed and the algorithm is unconditionally stable. A numerical example is given to demonstrate the validity and efficiency of the proposed method. 展开更多
关键词 non-classically damped systems motion equation generalized SDOF complex oscillator state space theory unconditionally stable algorithm
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Some Properties of Solutions of Periodic Second Order Linear Differential Equations 被引量:1
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作者 Li Peng XIAO Zong Xuan CHEN 《Journal of Mathematical Research and Exposition》 CSCD 2011年第2期279-286,共8页
In this paper,the zeros of solutions of periodic second order linear differential equation y + Ay = 0,where A(z) = B(e z ),B(ζ) = g(ζ) + p j=1 b ?j ζ ?j ,g(ζ) is a transcendental entire function of l... In this paper,the zeros of solutions of periodic second order linear differential equation y + Ay = 0,where A(z) = B(e z ),B(ζ) = g(ζ) + p j=1 b ?j ζ ?j ,g(ζ) is a transcendental entire function of lower order no more than 1/2,and p is an odd positive integer,are studied.It is shown that every non-trivial solution of above equation satisfies the exponent of convergence of zeros equals to infinity. 展开更多
关键词 periodic differential equation complex oscillation regular order of growth
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