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
Recent studies have shown that explosive synchronization transitions can be observed in networks of phase oscillators [Goemez-Gardenes J, Goemez S, Arenas A and Moreno Y 2011 Phys. Rev. Lett. 106 128701] and chaotic o...Recent studies have shown that explosive synchronization transitions can be observed in networks of phase oscillators [Goemez-Gardenes J, Goemez S, Arenas A and Moreno Y 2011 Phys. Rev. Lett. 106 128701] and chaotic oscillators [Leyva I, Sevilla-Escoboza R, Buldu J M, Sendifia-Nadal I, Goemez-Gardefies J, Arenas A, Moreno Y, Goemez S, Jaimes-Reaitegui R and Boccaletti S 2012 Phys. Rev. Lett. 108 168702]. Here, we study the effect of different chaotic dynamics on the synchronization transitions in small world networks and scale free networks. The continuous transition is discovered for R6ssler systems in both of the above complex networks. However, explosive transitions take place for the coupled Lorenz systems, and the main reason is the abrupt change of dynamics before achieving complete synchronization. Our results show that the explosive synchronization transitions are accompanied by the change of system dynamics.展开更多
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
Ⅰ. INTRODUCTIONThe model of the harmonic oscillator with complex frequency is very valuable for the study of the dissipation theory in physics. The model of the dissipation and nuclear friction can be seen as particu...Ⅰ. INTRODUCTIONThe model of the harmonic oscillator with complex frequency is very valuable for the study of the dissipation theory in physics. The model of the dissipation and nuclear friction can be seen as particular cases of the harmonic oscillator with complex frequency.展开更多
Betweenness centrality is taken as a sensible indicator of the synchronizability of complex networks. To test whether betweenness centrality is a proper measure of the synchronizability in specific realizations of ran...Betweenness centrality is taken as a sensible indicator of the synchronizability of complex networks. To test whether betweenness centrality is a proper measure of the synchronizability in specific realizations of random networks, this paper adds edges to the networks and then evaluates the changes of betweenness centrality and network synchronizability. It finds that the two quantities vary independently.展开更多
Complex networks have been extensively investigated in recent years.However,the dynamics,especially chaos and bifurcation,of the complex-valued complex network are rarely studied.In this paper,a star network of couple...Complex networks have been extensively investigated in recent years.However,the dynamics,especially chaos and bifurcation,of the complex-valued complex network are rarely studied.In this paper,a star network of coupled complex-valued van der Pol oscillators is proposed to reveal the mechanism of star coupling.By the aid of bifurcation diagram,Lyapunov exponent spectrum and phase portrait in this study,chaos,hyper-chaos,and multi-existing chaotic attractors are observed from the star network,although there are only periodic states in a complex-valued van der Pol oscillator.Complexity versus coupling strength and nonlinear coefficient shows that the bigger the network size,the larger the parameter range within the chaotic(hyper-chaotic)region.It is revealed that the chaotic bifurcation path is highly robust against the size variation of the star network,and it always evolves to chaos directly from period-1 and quasi-periodic states,respectively.Moreover,the coexistence of chaotic phase synchronization and complete synchronization among the peripherals is also found from the star network,which is a symmetrybreaking phenomenon.展开更多
Using a model anharmonic oscillator with asymptotically decreasing effective mass to study the effect of compositional grading on the quantum mechanical properties of a semiconductor heterostructure, we determine the ...Using a model anharmonic oscillator with asymptotically decreasing effective mass to study the effect of compositional grading on the quantum mechanical properties of a semiconductor heterostructure, we determine the exact bound states and spectral values of the system. Furthermore, we show that ordering ambiguity only brings about a spectral shift on the quantum anharmonic oscillator with spatially varying effective mass. A study of thermodynamic properties of the system reveals a resonance condition dependent on the magnitude of the anharmonicity parameter. This resonance condition is seen to set a critical value on the said parameter beyond which a complex valued entropy which is discussed, emerges.展开更多
基金the Deputyship for Research&Innovation,Ministry of Education in Saudi Arabia for funding this research work through the project number RI-44-0143
文摘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.
基金supported by the National Natural Science Foundation of China (Grant Nos. 61203159,61164020,11271295,and 11071280)the Foundation of Wuhan Textile University (Grant No. 113073)
文摘Recent studies have shown that explosive synchronization transitions can be observed in networks of phase oscillators [Goemez-Gardenes J, Goemez S, Arenas A and Moreno Y 2011 Phys. Rev. Lett. 106 128701] and chaotic oscillators [Leyva I, Sevilla-Escoboza R, Buldu J M, Sendifia-Nadal I, Goemez-Gardefies J, Arenas A, Moreno Y, Goemez S, Jaimes-Reaitegui R and Boccaletti S 2012 Phys. Rev. Lett. 108 168702]. Here, we study the effect of different chaotic dynamics on the synchronization transitions in small world networks and scale free networks. The continuous transition is discovered for R6ssler systems in both of the above complex networks. However, explosive transitions take place for the coupled Lorenz systems, and the main reason is the abrupt change of dynamics before achieving complete synchronization. Our results show that the explosive synchronization transitions are accompanied by the change of system dynamics.
文摘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.
文摘Ⅰ. INTRODUCTIONThe model of the harmonic oscillator with complex frequency is very valuable for the study of the dissipation theory in physics. The model of the dissipation and nuclear friction can be seen as particular cases of the harmonic oscillator with complex frequency.
基金supported by the National Natural Science Foundation of China (Grant Nos. 60870013 and 10832006)
文摘Betweenness centrality is taken as a sensible indicator of the synchronizability of complex networks. To test whether betweenness centrality is a proper measure of the synchronizability in specific realizations of random networks, this paper adds edges to the networks and then evaluates the changes of betweenness centrality and network synchronizability. It finds that the two quantities vary independently.
基金the National Natural Science Foundation of China(Grant No.61773010)。
文摘Complex networks have been extensively investigated in recent years.However,the dynamics,especially chaos and bifurcation,of the complex-valued complex network are rarely studied.In this paper,a star network of coupled complex-valued van der Pol oscillators is proposed to reveal the mechanism of star coupling.By the aid of bifurcation diagram,Lyapunov exponent spectrum and phase portrait in this study,chaos,hyper-chaos,and multi-existing chaotic attractors are observed from the star network,although there are only periodic states in a complex-valued van der Pol oscillator.Complexity versus coupling strength and nonlinear coefficient shows that the bigger the network size,the larger the parameter range within the chaotic(hyper-chaotic)region.It is revealed that the chaotic bifurcation path is highly robust against the size variation of the star network,and it always evolves to chaos directly from period-1 and quasi-periodic states,respectively.Moreover,the coexistence of chaotic phase synchronization and complete synchronization among the peripherals is also found from the star network,which is a symmetrybreaking phenomenon.
文摘Using a model anharmonic oscillator with asymptotically decreasing effective mass to study the effect of compositional grading on the quantum mechanical properties of a semiconductor heterostructure, we determine the exact bound states and spectral values of the system. Furthermore, we show that ordering ambiguity only brings about a spectral shift on the quantum anharmonic oscillator with spatially varying effective mass. A study of thermodynamic properties of the system reveals a resonance condition dependent on the magnitude of the anharmonicity parameter. This resonance condition is seen to set a critical value on the said parameter beyond which a complex valued entropy which is discussed, emerges.
