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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,...
The paper firstly analyzes a four-wing chaotic attractor which is reported recently. Then, a fractional-order chaotic attractor can be obtained based on the four-wing chaotic system. When vary, the dynamics of the fractional-order chaotic attractor are very complex, not only can the four-wing chaotic attractor be observed by numerical simulation, but also some typical periodic attractors can be found...
A new chaotic attractor is discovered. The heteroclinic orbits in the new system has been found by using the undermined coefficient method. It analytically demonstrates that there exists one heteroclinic orbit of the Si'lnikov type that connects two nontrivial equilibrium points, and therefore Smale horseshoes and the horsesheos chaos occur for this system via the Si'likov criterion. The convergence...
In this paper, a new hyper-chaotic system is generated by introducing a state variable into Chen system. This system contains five system parameters and two cross-product terms, can generate hyper-chaotic attractors with proper parameters regions. The theoretical analysis demonstrates that a Hopf bifurcation arises at zero equilibrium point. The basic dynamic properties of the proposed system are...
The paper firstly analyzes a three-wing or four-wing chaotic attractor which is reported recently. When vary, the dynamics of the chaotic attractor are very complex, not only can the three-wing or four-wing chaotic attractor be observed by numerical simulation, but also some typical periodic attractors can be found. In addition, an analog circuit is also made for the three-wing or four-wing chaotic...
This paper presents a new four dimensional autonomous hyper-chaotic system which contains four quadratic terms and five system parameters. The proposed system has complex dynamical behaviors, can generate a four-wing hyper-chaotic attractor with proper parameters ranges. The theoretical analysis and numerical analysis demonstrate that a Hopf bifurcation arises at zero equilibrium point. Finally, an...
In order to generate complex chaotic attractor, an auto-switched chaotic system which consists of two subsystems is constructed. The switched chaotic system can change its behavior automatically from one to another via a data selector. The system is also implemented based on FPGA by EDA Technology, and the experiments shows a good agree with simulation.
Based on the well-known topological horseshoe theorem, a new rigorous computer-assisted proof for the existence of topological horseshoe in Chen's attractor is given. An appropriate Poincare section of Chen's attractor is chosen to obtain the corresponding Poincare map which is proved to be semi-conjugate to a 2-shift map. This implies that Chen's attractor has positive topological entropy, thus in...
In this paper, a novel four-dimensional (4D) autonomous continuous time Hopfield-type neural network with two parameters is investigated. Computer simulations show that the 4D Hopfield neural network has rich and funny dynamics, and it can display equilibrium, periodic attractor, chaotic attractor and quasi-periodic attractor for different parameters. Moreover, when the system is chaotic, its positive...
The paper analyzes a new hyper-chaotic Lu attractor which has rich and complex dynamical behaviors, by utilizing Lyapunov exponent spectrum, bifurcation diagram and phase portraits. And the local bifurcation is investigated by the centre manifold theorem. With the variation of parameters, the system will undergo pitchfork bifurcation and Hopf bifurcation at zero equilibrium, respectively. Finally,...
This paper simply analyses a hyper-chaos system which based on the modified Lorenz system, and chiefly designs its circuit. In this paper, the different phase portraits of the system are studied when the system parameter k is varied. The circuit of the system is implemented by the operational amplifiers and the analog multiplier, it includes four channels. Some phase portraits can be observed through...
The current famous topological horseshoe theory is applied to an SEIR epidemic model with sinusoidally varying contact rate. For the first time, a rigorous computer-assisted verification of the existence of horseshoe chaos in this SEIR model is presented, which implies that chaos does exist from a theoretical and mathematical viewpoint other than the purely numerical computations viewpoint. By virtue...
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