Integer-order and fractional-order multifunctional chaotic experiment instrument

Abstract

The invention discloses an integer-order and fractional-order multifunctional chaotic experiment instrument, which can be used for realizing experiment of a three-dimensional or four-dimensional integer-order or fractional-order chaotic system and can output a time-sequence diagram or a phase diagram by a dual-trace oscilloscope. The integer-order and fractional-order multifunctional chaotic experiment instrument comprises a shell and an internal circuit board, wherein the internal circuit board is arranged in the shell; the internal circuit board is provided with a power circuit, an I-part circuit and an II-part circuit; the I-part circuit and the II-part circuit are used for generating chaotic signals and are the same in circuit structure; each part consists of four channels; each channel comprises a signal input circuit, an adder circuit, an integral circuit and a chaotic signal output circuit; each adder circuit is respectively connected with the corresponding signal input circuit and the corresponding integral circuit; and the output end of each integral circuit is connected with the corresponding chaotic signal output circuit. The integer-order and fractional-order multifunctional chaotic experiment instrument disclosed by the invention is simple and reasonable in structure, good in stability, high in reliability and strong in practicability, can be used for teaching in a physical laboratory of the college, can also be used as common scientific and research equipment of the research institutions, and completely meets the research need of the current chaotic phenomenon.

Description

technical field [0001] The invention belongs to an instrument for demonstrating and testing various chaos experiments in physics and mathematics research and teaching, and in particular relates to a multifunctional chaos tester of integer order and fractional order. Background technique [0002] Chaos is a ubiquitous phenomenon in nature, and it is a research hotspot in the field of nonlinear dynamics. Since the 1970s, especially since the 1990s, the research has achieved unprecedented results. However, the applied research of chaos lags far behind the level of theoretical research. At present, the experimental tests of chaos and ultra-chaos are all realized by circuits, but there is no comprehensive chaos experimental instrument in laboratories and research institutions. The chaos experimental instruments used in our country's laboratories mainly include the nonlinear chaos experimental instrument researched by Shanghai University. This experimental instrument uses a doubl...

AI Technical Summary

Problems solved by technology

The chaos experimental instruments used in our country's laboratories mainly include the nonlinear chaos experimental instrument researched by Shanghai University. This experimental instrument uses a double operational amplifier to form a negative resistance circuit, and a nonlinear circuit composed of other resistance-capacitance components to realize the Chua's circuit. Chaos demonstration function, but for other systems, such as lorenz system, liu system, lü system, etc., it cannot be demonstrated experimentally. As for the demonstration and test of other high-dimensional and fractional order systems, it is even more impossible to realize

Other chaos experiments are mainly built with discrete components, which is time-consuming and labor-intensive, and has poor general performance. For example, a well-made circuit board can only be used for chaos experiments of a certain system. When the parameters of the system change, the circuit has to be redesigned. One is to use circuit simulation software for simulation. Although the current circuit simulation software is better, there is still a big gap compared with the circuit composed of actual components.

Therefore, there is no chaos experimental instrument that can synthesize the current common chaotic systems and can adapt to the new system by changing the meta-parameters slightly.

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