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Chaotic maps with higher chaotic complexity are urgently needed in many application scenarios. This paper proposes a chaotification model based on sine and cosecant functions (CMSC) to improve the dynamic properties of existing chaotic maps. CMSC can generate a new map with higher chaotic complexity by using the existing one-dimensional (1D) chaotic map as a seed map. To discuss the performance of CMSC, the chaos properties of CMSC are analyzed based on the mathematical definition of the Lyapunov exponent (LE). Then, three new maps are generated by applying three classical 1D chaotic maps to CMSC respectively, and the dynamic behaviors of the new maps are analyzed in terms of fixed point, bifurcation diagram, sample entropy (SE), etc. The results of the analysis demonstrate that the new maps have a larger chaotic region and excellent chaotic characteristics.

In this study, field-programmable gate array (FPGA)-based hardware implementation of the wavelet neural network (WNN) training using particle swarm optimization (PSO) and improved particle swarm optimization (iPSO) algorithms are presented. The WNN architecture and wavelet activation function approach that is proper for the hardware implementation are suggested in the study. Using the suggested architecture and training algorithms, test operations are implemented on two different dynamic system recognition problems. From the test results obtained, it is observed that WNN architecture generalizes well and the activation function suggested has approximately the same success rate with the wavelet function defined in the literature. In the FPGA-based implementation, IEEE 754 floating-point number format is used. Experimental tests are done on Xilinx Artix 7 xc7a100t-1csg324 using ISE Webpack 14.7 program.

Real biological neurons are dynamical systems that can process a nonlinear, arbitrary input signal with a dynamic threshold voltage, exhibit refractory time, and have a smooth $F$–$I$ curve. This paper presents a generalized bio-plausible neuron model with refractoriness, frequency adaptation, and dynamic threshold. The spiking characteristics of the generalized neuron are enhanced with less circuitry and fewer parameters compared to older circuits. The proposed silicon neuron can generate all known spiking behaviors, just like a biological neuron. The circuit is designed using a 180 nm standard CMOS process. The entire design uses 22 transistors with a total power consumption of only 2 nW for a 1 nA step current at a spike frequency of 122 Hz. The power consumption and spike frequency rate depend on the input current. The proposed neuron is also capable of displaying both Type I and Type II frequency response characteristics. In addition, our neuron model underwent Monte Carlo simulation with 1000 sample runs to assess its robustness and stability against process variations and uncertainties. The results indicate that the average energy consumption of the proposed neuron model falls within the range of 16 pJ to 68 pJ.

This paper analyzes the convergence properties and convergence region of a class of trajectory-based power flow methods. The convergence region of the trajectory-based method is a connected set and possesses the near-by property. The convergence region of Newton method and trajectory-based method in solving power flow problems are numerically investigated. Since the convergence region of trajectory-based method corresponds to the stability region of the nonlinear dynamic system, the stability regions of two dynamic systems are computed. The numerical results indicate that the stability region of the dynamic system possesses better geometry features than the convergence region of Newton method. These properties make the trajectory-based power flow method robust, especially on heavy loading conditions.

In this work, the linear and nonlinear dynamics of thermal convection in an incompressible Newtonian (alumina-copper)/water hybrid nanofluid each confined in an infinite rectangular cavity and heated from below via the Cattaneo–Christov heat flux model are studied for volume fractions fixed between 0 and 0.05. Firstly, using the governed flow equations and free boundary conditions, we proceed to the classical theory of stationary and oscillatory convection which help us to find the expressions of critical Rayleigh numbers, Cattaneo numbers and wavenumber of base fluid as a function of mono or hybrid nanofluid thermophysical properties. The results show that when the Cattaneo number increases, the critical Rayleigh number is constant in the case of stationary convection but decreases in the case of oscillatory convection for pure base fluid and hybrid nanofluids. It is noted that beyond the threshold Cattaneo number, the critical Rayleigh number of stationary convection is greater than those of oscillatory convection and the critical wavenumber shifts discontinuously from stationary to oscillatory convection. Secondly, the use of the truncated Galerkin approximation made it possible to find a five low-dimensional system in order to study numerically the transition from natural convection to chaotic behavior of nanofluid. We noticed that the addition of hybrid nanoparticle in the heat fluid transfer increases the domain of stationary convection by delaying the oscillatory convection with increasing normalized Rayleigh number. Also, the bifurcation diagrams show that the use of hybrid nanoparticles allows further control of the chaos in base fluid by expanding the convective flow. Furthermore, in the presence of thermal relaxation time, the chaos in the hybrid nanofluid lasts longer compared to the ordinary fluid.

We investigated the generation of spherical continuous-tilings of the chaotic attractors or the filled-in Julia sets from the plane mappings. We build three plane mappings, which can be used to construct the continuous patterns on the surfaces of the hexahedron and the unit sphere. We discuss the coordinate transformation for a spatial point between the different coordinate systems and further discuss how to project a spherical point onto a surface of the inscribed hexahedron. We present a method of constructing a spherical pattern with the pattern of a square on the inscribed hexahedron from an arbitrary projective angle, and generate spherical patterns from the three plane mappings. The results show that we can construct a great number of spherical patterns of the chaotic attractors and the filled-in Julia sets from the plane mappings, which are based on the square lattice and meet the requirements of the continuity and the four rotation symmetries on the lattice's boundaries.

The neutral delay model has many applications in biology, ecology, man-made neural networks, mechanics and engineering. The main purpose of this paper is to establish new oscillation criteria for the two-dimensional neutral delay dynamical system

Systems can be classified as dynamic or static depending on the nature of the performance. A static system has a fixed target value for the performance characteristic while a dynamic system has a variable performance characteristic. This variable characteristic can be adjusted by a signal factor based on the requirement of the user. Due to this nature, modeling and optimization methods of dynamic systems may be different from those for static systems. This paper presents a two-step approach to the optimization modeling and design of linear dynamic systems. The approach is based on the concepts of quality engineering, experimental design, loss function, signal-to-noise (SN) ratio and optimization methodology. The motivation, justification and computation of SN ratios for linear dynamic systems will be discussed. As an illustrative example, a circuit design problem is given to demonstrate the method.

The identification of damping in a structural system is extremely important for reliable prediction of response of dynamic systems. The present study focuses on the damping parameters identification of linear multi-degree of freedom (MDOF) systems defined by Rayleigh damping model. A system identification (SI) algorithm based on the free vibration response of structures is proposed to identify the damping parameters. In doing so, the equation error based SI approach is readily developed for identification of damping properties at element level. The formulation is elucidated using numerically simulated modal data obtained through finite element analysis. The robustness of the algorithm is also studied by Monte Carlo simulation based error sensitivity analysis. The identified damping values are found to be in consistent with those of pre-assigned values used to simulate modal data.

Lunar-based equipment undertakes the task of movement and transportation in the construction of unmanned lunar base. In the process of moving, the mechanical legs of the equipment are influenced by the lunar soil with special mechanical properties. In order to avoid these uncertainties caused by the lunar soil and other lunar environmental conditions affecting the safety during the mission, a new robust control method with the form of sectionalized expression is proposed based on the dynamic model of the leg-soil system. Lyapunov second method is introduced to demonstrate that the proposed control method can maintain the stability of the leg-soil system successfully. In order to clarify the contact force in the dynamics model, CAS-1 lunar soil simulant that can accurately simulate real lunar soil is used in the calibration test to obtain the precise mechanical parameters. Simulation and experiment are also carried out to verify the proposed control method and the traditional control methods are introduced to make a comparison. Both the simulation and experiment results show that the proposed control method has a better control effect than traditional methods. The proposed method improves the accuracy by an average of 75.7% and 55.9% compared to the traditional methods and the error is limited to 0.2%. By maintaining the stability and accuracy of the leg-soil system, the stability of the lunar-based equipment is improved when performing construction tasks. This study lays the foundation for the construction of unmanned lunar base in advance.

In competitive sports, players are always at high risk for injuries. Sports injuries in rugby sports are directly related to the team’s game performance, especially when the player has an old sports injury or psychological stress. By considering the athlete as a dynamic system and quantifying the features associated with sports injuries, machine learning can be used to predict and assess the associated risks. In this paper, a simplified GRU is proposed to construct the mapping relationship between sports injury features and rugby game results. The comparison experiments with other machine learning models show that this model has better robustness in the prediction tasks of sports injuries and competition results of teenage rugby players.

This paper is devoted to nonlinear phenomena in economics which arise in a monopoly.