Fractal structures in a generalized squared map with exponential terms are expanded in this paper. We describe how complex behaviors can arise as the parameters change. The appearances of different kinds of fractal st...Fractal structures in a generalized squared map with exponential terms are expanded in this paper. We describe how complex behaviors can arise as the parameters change. The appearances of different kinds of fractal structures, in both the attractive and the divergent regions, and most interestingly, on small regular islands embedded in the chaotic region, are manifested to have a variety of extraordinary geometries in the parameter plane.展开更多
This paper proposes a new robust chaotic system of three-dimensional quadratic autonomous ordinary differential equations by introducing an exponential quadratic term. This system can display a double-scroll chaotic a...This paper proposes a new robust chaotic system of three-dimensional quadratic autonomous ordinary differential equations by introducing an exponential quadratic term. This system can display a double-scroll chaotic attractor with only two equilibria, and can be found to be robust chaotic in a very wide parameter domain with positive maximum Lyapunov exponent. Some basic dynamical properties and chaotic behaviour of novel attractor are studied. By numerical simulation, this paper verifies that the three-dimensional system can also evolve into periodic and chaotic behaviours by a constant controller.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No.11161027)the Natural Science Foundation of Gansu Province,China (Grant No. 1010RJZA067)
文摘Fractal structures in a generalized squared map with exponential terms are expanded in this paper. We describe how complex behaviors can arise as the parameters change. The appearances of different kinds of fractal structures, in both the attractive and the divergent regions, and most interestingly, on small regular islands embedded in the chaotic region, are manifested to have a variety of extraordinary geometries in the parameter plane.
文摘This paper proposes a new robust chaotic system of three-dimensional quadratic autonomous ordinary differential equations by introducing an exponential quadratic term. This system can display a double-scroll chaotic attractor with only two equilibria, and can be found to be robust chaotic in a very wide parameter domain with positive maximum Lyapunov exponent. Some basic dynamical properties and chaotic behaviour of novel attractor are studied. By numerical simulation, this paper verifies that the three-dimensional system can also evolve into periodic and chaotic behaviours by a constant controller.
