Continuous-time memristors have been used in numerous chaotic circuit systems. Similarly, the discrete memristor model applied to a discrete map is also worthy of further study. To this end, this paper first proposes a discrete memristor model and analyzes the voltage–current characteristics of the memristor. Also, the discrete memristor is coupled with a one-dimensional (1D) sine chaotic map through different coupling frameworks, and two different two-dimensional (2D) chaotic map models are generated. Due to the presence of linear fixed points, the stability of the 2D memristor-coupled chaotic map depends on the choice of control parameters and initial states. The dynamic behavior of the chaotic map under different coupled map frameworks is investigated by using various analytical methods, and the results show that different coupling frameworks can produce different complex dynamical behaviors for memristor chaotic maps. The dynamic behavior based on parameter control is also investigated. The numerical experimental results show that the change of parameters can not only enrich the dynamic behavior of a chaotic map, but also increase the complexity of the memristor-coupled sine map. In addition, a simple encryption algorithm is designed based on the memristor chaotic map under the new coupling framework, and the performance analysis shows that the algorithm has a strong ability of image encryption. Finally, the numerical results are verified by hardware experiments.
There are few reports on the nondestructive adjustment of the oscillation amplitude of the chaotic sequence in the discrete map. To study the lossless regulation of the oscillation amplitude of chaotic sequences, this article proposes a new simple two-dimensional (2D) hyperchaotic map with trigonometric functions. It not only exhibits contains the offset boosting bifurcation and offset boosting coexistence attractors, but also realizes the offset boosting of two state variables with respect to arbitrary parameters in the 2D map. The simulation results of bifurcation diagram, maximum Lyapunov exponent and attractor phase diagram show that the map can produce complex dynamical behaviors. In addition, the introduction of new control parameters into the 2D hyperchaotic chaotic map can also make the hyperchaotic map exhibit rich multistable phenomena. At the same time, the common change of the initial state and the control parameters can realize the arbitrary switching and co-existence of the attractor in the phase plane. In the end, the 2D hyperchaotic map was tested and verified by hardware experiment platform.
Underground coal gasification (UCG) is a highly efficient new type of coal mining technology with broad future prospects. In order to study the cavity extension formation in the early ignition stage of UCG, a block coal scale UCG simulation experiment was carried out. The results show that after the ignition, the temperature above ignition point rose fastest, and the coal combustion interface and high temperature area moved toward to the above of ignition point, while the temperature of the left and right sides of ignition point rose a little slowly. According to the results of dissected block coal, it is indicated that the extension scale in the vertical direction was significantly larger than other directions; the combustion cavity form was an irregular rectangle like a pear. The results of this experiment revealed the cavity extension process from ignition of UCG channels to the formation of cavity, which provided a foundation for the study of extension characteristics of UCG channel in the entire UCG process.
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