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In this paper, a Cauchy problem for two-dimensional Lap lace equation in the strip is considered. This is a classical severely ill-posed problem. Connecting Shannon wavelet bases with a spectral integral of the Hermitian operator, we can obtain a regularized solution. Moreover, some sharp stable estimates between the exact solution and it's approximation is also provided.
In this paper, a partial dependent prey-predator model with discrete and distributed delays is studied by using the theory of functional differential equation and Hassard's method, the conditions on which positive equilibrium exists and Hopf bifurcation occurs are given, finally, numerical simulations are also included.
A seven-mode truncation system of the Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is considered. Its stationary solutions and stability are presented, the existence of attractor and the global stability of the system are discussed. The whole process, which shows a chaos behavior approached through an involved sequence of bifurcations, is simulated numerically by computer...
In this paper, upon the nonlinear Korteweg-de Vries(KdV) equation, controlling the amplitude of nonlinear Ross by waves, which was induced by nonlinear effect of and nonlinear effect of topography, the numerical solution was gotten using the numerical method.
This paper is concerned with chaos in a delay difference equation. The map of the system is proved to be chaotic in the sense of both Devaney and Li-Yorke under some conditions, by employing the snap-back repeller theory. Some computer simulations are provided to illustrate the theoretical result.
The simplified quasi-cubics function is used quite common in the ordinary differential equation, which is used to describe the biological neuron model. As complexity of the biological neuron model, its analytical solution hardly can be solved in common situation. Numerical solution of the model is very important in reality. Three fast convergence methods are proposed for the simplified function by...
An SEIR model with varying total population size and continuous vaccination is proposed. The stability of the disease-free equilibrium is discussed, and the global stability of the disease-free equilibrium is discussed with the Lasalle's invariance principle. Using analytical methods, the existence and uniqueness of the positive equilibrium are obtained, and it's stability is also discussed by Routh-Hurwith...
In this paper, we study mean first-passage time (MFPT) for random walks on a network through edge iteration. The feature of this kind of network is that every existing edge gives birth to finite nodes at each step. According to the network structures, we obtain the analytical expression for MFPT, which shows that the MFPT grows as a power-law function with the number of nodes in the large limit of...
To enhance the complexity of the chaos, improve the characteristics of chaos, and increase the number of chaotic types, a simple method is put forward in this paper. This method does not need to change the existing chaotic system, but just makes a nonlinear transformation to the chaotic signal by a unary polynomial. The nonlinear transformation has the characteristic that its physical circuit is easy...
Based on the chaos anti-control theory, a new Lorenz hyper chaotic system family is proposed by adding a linear controller to the three dimensional autonomous Lorenz system family in this paper. It has been verified that the systems in the newly proposed family have the possibility of hyper chaos by analyzing their symmetry, dissipation, the stability of their equilibrium points, as well as the Lyapunov...
In this paper, a delayed predator-prey model incorporating a constant prey refuge and diffusion is studied. By analyzing the characteristic equation of linearized system corresponding to the model, we study the local asymptotic stability of the postive equilibrium of the system. Hopf bifurcation is occured. By using the normal form and the center manifold theory, an explicit algorithm to determine...
Renewable power generation systems are gaining popularity and have developed quickly in recent years. However, due to the intermittent features of the renewable energy sources, conversion systems involving more than one energy sources are usually designed with multiple structures and multiple operating modes. The dynamic behavior is thus quite complex, and the design for stable operation of such systems...
This article investigates the dynamical behavior in the fractional-order permanent magnet synchronous motor, firstly. Secondly, based on the Lyapunov equation stability theory of fractional-order systems, we scheme out corresponding controller, and realized the control of permanent magnet synchronous motor. And then Routh-Hurwitz conditions and numerical simulations are used to show the agreement...
The motor control has progressed into more advanced PLC and MCU control system from the original relay control system. Currently, the thought of chaos control and chaos anti-control is budding. New information technology on the control of the motor, based on chaotic neural network, has higher stability, accuracy and reliability. While chaos control and anti-control can be used in pattern classification,...
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