A New Type Of Chaotic System With Hidden Properties

Chaos science,as a multi-disciplinary interdisciplinary subject,can be found in several fields.Chaotic systems play a pivotal role in the application of secure communication systems,so the theoretical study of chaotic systems has a profound significance.With the introduction of the concept of hidden attractor,the modeling of chaotic systems with hidden properties and their dynamics analysis have become a hot research topic.At present,most of the studies on chaotic systems are mainly focused on dissipative chaotic systems,while the modeling and dynamics analysis of conservative systems with hidden properties are less studied.Compared with integerorder nonlinear systems,fractional-order nonlinear systems can more accurately describe the complex dynamical behaviors that occur in actual systems.The modeling and analysis of fractional-order chaotic systems,especially the construction of systems with special dynamical properties,has important theoretical significance and potential engineering applications.Based on the above research background,this dissertation respectively proposes an integer-order four-dimensional non-Hamiltonian conservative hyperchaotic system and its chaotic model in fractional form based on a simple mathematical model of a three-dimensional memristor circuit.The constructed integer-order conservative system has no-equilibrium point hiding property,and the hidden dynamical behavior of the system is investigated in depth by numerical simulation methods such as Lyapunov exponent,fractional dimension,bifurcation diagram and spectral entropy for two cases of system parameters and initial value change,respectively.The results show that the integer-order system has a wider chaotic region and higher spectral entropy compared to the existing chaotic systems.The fractional-order chaotic system constructed by introducing the fractional-order differential operator defined by Caputo can exhibit three initial offset boosting behaviors with different characteristics by changing the initial values with fixed parameters.In terms of verifying the numerical simulation results,the verification platform is built using improved analog circuit design and digital signal processing techniques,respectively,and the results demonstrated by the verification platform are highly consistent with the numerical simulation results,thus proving the physical realizability of the integer-order and fractional-order chaotic systems,respectively.In terms of hidden memristive chaotic systems,this dissertation proposes a fourdimensional no-equilibrium point hidden chaotic system based on the mathematical model of magnetron memristor,which exhibits a multi-wing behavior different from the existing wing-like attractor and shows the dynamical behavior of hidden extreme multi-stability and three-state transient transition under specific parameters and initial values.By analyzing the time domain of each state variable of the system,the homogeneous phase trajectory transition behavior is also found.The system is implemented by digital signal processing technology,which demonstrates the physical realizability of the multi-wing system and creates conditions for its subsequent engineering applications.