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This paper is concerned with the ultimate bounds and positively invariant sets for a system describing the amplitude of a plasma instability proposed by Pikovski, Rabinovich and Trakhtengerts. Based on generalized positive definite and radially unbound Lyapunov functions with respect to the parameters of the system, we derive a new ellipsoidal estimate and a cylindrical domain of the globally exponentially...
This paper introduces several basic principles of chaos generated by memristive circuits in accordance with the characteristic of memristor, and a new three-dimensional chaotic system with only one equilibrium are further proposed based on a series memristive circuit. The numerical results show that the proposed memristive system has the common features of nonlinear system under different parameters,...
With the further research of nonlinear systems, we have discovered that many practical physical circuits contain chaotic phenomenon. At the same time, a number of control schemes can be used to controlled chaotic system, such as control by Ott-Grebogi-Yorke (OGY) method, control by delayed feedback control (DFC) method, control by synchronization and so on. Delayed feedback control was proposed by...
This paper considers the sub shifts induced by a class of non-primitive constant-length substitutions on two symbols. The authors give a sufficient condition for hyperspace system induced by such a sub shift to be Li-Yorke chaotic. Furthermore, the authors proof a sufficient condition for the hyperspace system mentioned above to have 0 topological entropy.
In this paper, the Genesio system with distributed time delay feedback is studied. Its linear stability is investigated based on the Routh-Hurwitz criteria. After the local asymptotic stability is analyzed, Hopf bifurcation is demonstrated by choosing the mean time delay as a bifurcation parameter. The direction and the stability criteria of the bifurcating periodic solutions are determined by applying...
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.
In this paper, iteration method of logistic map with low positions is introduced in order to investigate property of logistic map. Basic structure of logistic map is proposed, which consists of common gene positions (CGPs) and individual gene positions (IGPs). CGPs have the same value of corresponding positions which transferred from previous numerical solutions. The ergodicity and long-term unpredictability...
In this paper, an existence result of positive solutions for some three-point boundary value problems is obtained by using Leray-Schauder nonlinear alternative.
Bifurcation of limit cycles for two differential polynomial systems is investigated using both qualitative analysis and numerical exploration. The investigation is based on detection functions which are particularly effective for the differential polynomial systems. The study reveals that each of the two systems has 8 limit cycles using detection function approach. By using method of numerical simulation,...
A new three-dimensional continuous quadratic autonomous chaotic system with no equilibria is discussed. Basic properties of the new system are analyzed by means of Lyapunov exponent spectrum, Poincaré mapping, fractal dimension, Analysis results show that this system has complex dynamics with some interesting characteristics.
In this paper, we will discuss the oscillation of solutions of higher-order nonlinear delay dynamic equations on time scales, which have the following form $$S_n^\Delta(t, x)+p(t)f(x(\tau(t)))=0.$$ We will establish some oscillation criteria for these dynamic equations. Our results improve some previously obtained ones.
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...
In this work, we provide a practical implementation of a new memristor based chaotic circuit, which was generated by replacing the nonlinear resistor in the canonical Chua's circuit with a flux-controlled memristor. The existence of the chaos is not only demonstrated by computer simulations, but also verified with Lyapunov exponents and bifurcation analysis. Moreover, we present a breadboarded circuit...
This Paper explores using a non-linear system to construct dynamic logic architecture-cellular neural networks (CNN). The proposed CNN schemes can discriminate the two input signals and switch easily among different 16 kinds of operational roles by changing parameters. Each logic cell performs more flexibly, that makes it possible to achieve complex logic operations and construct computing architecture...
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...
This study examines some dynamical behaviors, in simulations of financial systems. A new fractional-order financial system is proposed in this study. It is a generalization of a dynamic financial model recently reported in the literature. The basic dynamical behaviors of this financial system are investigated, such as the equilibrium, stability. Furthermore, it has been found that chaos exists in...
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...
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