Complex Dynamic Behavior Research Articles

Dynamics and implementation of a functional neuron model with hyperchaotic behavior under electromagnetic radiation

Prolonged exposure to electromagnetic radiation (EMR) may be hazardous to human health and plays a key role in the medical diagnosis of some diseases. And this effect can be better demonstrated by constructing a neuron model of EMR. Flux-controlled memristors can estimate the effects of EMR on neurons. In this work, a discrete flux-controlled memristor is used to estimate the behavior of EMR. Furthermore, the memristor is introduced into a neuron model to explore the effects of EMR on the behavior of neurons. The rich and interesting complex dynamical behavior of the model is investigated using analytical methods from nonlinear theory, including plotting bifurcation diagrams, Lyapunov exponent spectra (LEs) and complexity. By modulating the electromagnetic induction strength k of the memristor, it was observed that the introduction of EMR is able to generate hidden hyperchaotic attractors and initial-boosted behavior. The constructed neuron model is implemented based on a DSP platform. Pseudo random number generators (PRNGs) are further designed and the NIST test results illustrate the excellent random performance of the sequences generated by the neuron model. The properties exhibited in the neuron model under EMR provide a reference solution for EMR in the diagnosis and treatment of certain diseases.

Abundant families of Jacobi elliptic function solutions and peculiar dynamical behavior for a generalized derivative nonlinear Schrödinger equation employing extended F-expansion method

Abstract This study investigates a generalized derivative nonlinear Schrödinger (GDNLS) equation , demonstrating how ultrashort pulses propagate in a single-mode optical fiber. The extended F-expansion method, which is a modification of Kudryashov’s auxiliary equation approach, is applied in this investigation to generate Jacobi elliptic solutions for the GDNLS. Three distinct solution instances are examined, and a variety of explicit solutions, including breathers, solitary waves, bright/dark solitons, bright-dark interaction solitons, a soliton-like solution, and a rogue-like solution, are obtained. To demonstrate the complex dynamical behavior of GDNLS equation, several representative solutions are chosen and their moduli are shown in three-dimensional, two-dimensional, and contour plots using Maple software.

Touch-down condition control for the bipedal spring-mass model in walking.

Behaviors of animal bipedal locomotion can be described, in a simplified form, by the bipedal spring-mass model. The model provides predictive power, and helps us understand this complex dynamical behavior. 
In this paper, we analyzed a range of gaits generated by the bipedal spring-mass model during walking, and proposed a stabilizing touch-down condition for the swing leg. This policy is stabilizing against disturbances inside and outside the same energy level and requires only internal state information. In order to generalize the results to be independent of size and dimension of the system, we nondimensionalized the equations of motion for the bipedal spring-mass model. We presented the equilibrium gaits (a.k.a fixed point gaits) as a continuum on the walking state space showing how the different types of these gaits evolve and where they are located in the state space. Then, we showed the stability analysis of the proposed touch-down control policy for different energy levels and leg stiffness values. The results showed that the proposed touch-down control policy can stabilize towards all types of the symmetric equilibrium gaits. Moreover, we presented how the peak leg force change within an energy level and as it changes due to the type of the gait; peak force is important as a measurement of injury or damage risk on a robot or animal. Finally, we presented simulations of the bipedal spring-mass model walking on level ground and rough terrain transitioning between different equilibrium gaits as the energy level of the system changes with respect to the ground height. The analysis in this paper is theoretical, and thus applicable to further our understanding of animal bipedal locomotion and the design and control of robotic systems like ATRIAS, Cassie, and Digit.

Hidden complex multistable dynamical analysis and FPGA implementation of integer-fractional order memristive-memcapacitive chaotic system

Abstract A chaotic circuit based on a magnetic-controlled memristor and charge-controlled memcapacitor is proposed in this paper. The study reveals that it is a hyperchaotic system with hidden characteristics in integer-order. Furthermore, as the parameters change, the attractors exhibit rich evolutionary phenomena. Even after adjusting some parameters to very large values, the system still maintains hyperchaotic behavior. Interestingly, the basin of attraction shows the multistability of the system. Under initial value control, coexisting attractors are categorized into two types: those with initial offset-boosting behavior and nested attractors. When under parameter control, coexisting attractors are divided into two types: symmetric coexisting attractors and nested coexisting attractors. By analyzing the spectral entropy (SE) complexity of the system and using a complexity distribution diagram with two parameters and two initial values, the existence of multiple complex dynamic behaviors in the system has been verified. The fractional-order memristive-memcapacitive system based on the Grunwald-Letnikov algorithm and the five fractional-order values of q i (i = 1, 2, 3, 4, 5) are taken as different in the numerical simulation, it also displays multiple coexisting phenomena similar to those of the integer-order. Finally, Matlab/Simulink and DSP Builder software platform are used to design the fractional-order five-dimensional chaotic memristive-memcapacitive system, and then combined with VHDL and Verilog HDL hardware language, the proposed circuit system is verified on the EP4CE115F29C7 FPGA main chip of Cyclone IV E series. The consistency of hardware implementation and software simulation shows the correctness and feasibility of the design.

Design and synchronization control application of a new five-dimensional memristor CNN conservative hyperchaotic system

Abstract Incorporating memristors into a cellular neural network (CNN) and introducing chaotic characteristics can generate highly complex and unpredictable dynamic behaviors. To advance this research area, this paper proposes a new five-dimensional memristor CNN conservative hyperchaotic system and systematically analyzes its dynamic properties. The analysis content includes equilibrium point analysis, Poincaré sections, Lyapunov exponent spectra, bifurcation diagrams, two-parameter Lyapunov exponent spectra, complexity assessment, homogeneous and heterogeneous extreme multistability, etc In addition, the simulation circuit for the new system is designed and constructed. The digital circuit of the new system is implemented using a microcontroller (MCU). After running simulations, the experimental results from the analog circuit, digital circuit, and numerical simulation are consistent with each other, demonstrating the feasibility of the circuit implementation. Finally, two different synchronization control strategies are employed to achieve synchronization control within a finite time.

Single motor driven soft actuator design based on nonuniform sheering auxetic structure

Abstract Grasping functionality is one of the core functionalities that a manipulator needs to possess. Traditional rigid manipulators are typically composed of rigid materials. However, when dealing with objects of complex shapes, irregular surfaces, or soft materials, rigid manipulators often face challenges in effectively grasping and stably holding objects due to their rigidity, which can lead to damage or failure. To address these issues, constructing manipulators using soft actuators can be highly advantageous. In most current research, soft actuators are typically composed of flexible materials and fluids, which can result in highly complex dynamic behaviors and nonlinear characteristics. This complexity makes precise modeling and control of soft actuators more challenging, necessitating the use of advanced control algorithms and techniques to mitigate nonlinear effects. In this study, we first establish a mathematical model for the torsional and bending deformations of non-uniform shearing-auxetic structures. Subsequently, we validate the reliability of the mathematical model through simulation. Finally, we design a soft actuator that requires only single-motor control, which is based on the structural design of non-uniform shearing-auxetic structures. This type of soft actuator not only simplifies control aspects but also facilitates practical modeling and manufacturing processes. Moreover, it’s capable of achieving spiral grasping functionality.

Spatially Coded Transformations in Gradient‐Dependent Protocell Morphogenesis

AbstractChemical gradients provide spatiotemporal signaling fields in various cellular processes, driving complex dynamic behaviours such as differentiation and spatial organization. Here we employ opposing gradients of two artificial morphogens (sodium dodecyl sulfate (SDS) and sodium phosphotungstate (polyoxometalate; POM)) to systematically investigate morphological differentiation in organized populations of coacervate microdroplet‐based protocells. Using a matrix of 16 sets of counter‐diffusive gradients, we classify the differentiated protocells into five phenotypes and encode their spontaneous organization into different spatially patterned protocell consortia using a 3‐bit binary information system. We show that a predominant SDS gradient produces a diversity of differentiated phenotypes to generate complex spatially coded 2D protocell organizations. In contrast, a prevailing POM gradient decreases morphological differentiation, resulting in population homogenization. Our results improve our understanding of gradient concentration‐dependent collective responses in synthetic microscale agents and provide a step to a new spatially resolved information encoding method with 3‐bit binary outputs.

Statistical Properties of SIS Processes with Heterogeneous Nodal Recovery Rates in Networks

The modeling and analysis of epidemic processes in networks have attracted much attention over the past few decades. A major underlying assumption is that the recovery process and infection process are homogeneous, allowing the associated theoretical studies to be conducted in a convenient manner. However, the recovery and infection processes usually exhibit heterogeneous rates in the real world, which makes it difficult to characterize the general relations between the dynamics and the underlying network structure. In this work, we focus on the susceptible–infected–susceptible (SIS) epidemic process with heterogeneous recovery rates in a finite-size complete graph. Specifically, we study the metastable-state statistical properties of SIS epidemic dynamics with two different nodal recovery rates in complete graphs. We propose approximate solutions to the metastable-state expectation and the variance in the number of infected nodes within the framework of the mean-field approximation method. We also derive several upper and lower bounds of the steady-state probability that a node is in the infected state. We verify the proposed approximate solutions of the mean and variance via simulations. This work provides insights into the fluctuations in the statistical properties of epidemic processes with complex dynamical behaviors in networks.

Research on rigid-flexible coupling nonlinear dynamics of light commercial vehicle considering frame flexibility

Commercial vehicles play a vital role in the transportation industry. Generally, there will present a complex nonlinear dynamic behavior composed of periodic, quasi-periodic, and even chaotic vibration in vehicle vertical system under the continuous speed bump excitation. To explore the nonlinear dynamic behavior of vehicle system, a new rigid-flexible coupling nonlinear dynamic model for light commercial vehicle has been developed theoretically with considering the frame flexibility, suspension stiffness and damping nonlinearity, and rubber bushing nonlinearity. The dynamic model for frame and suspension have been developed with discrete element method and lumped mass method, respectively. Then, the flexible frame model has been verified through the mode shape and frequency calculated by finite element simulation. And the rigid-flexible coupling nonlinear dynamic model of a light commercial vehicle has been verified with Adams simulation and testing results. Furthermore, the influence of vehicle speed and the height of speed bump, suspension stiffness and damping, as well as cargo weight and distribution on vehicle system dynamics is analyzed with bifurcation diagram, time history, frequency, phase diagram and Poincare section. The results show the significant and complex effects on the nonlinear vibration of vehicle system, especially the nonlinear damping and the flexible frame.

A novel discrete memristive hyperchaotic map with multi-layer differentiation, multi-amplitude modulation, and multi-offset boosting.

In recent years, the introduction of memristors in discrete chaotic map has attracted much attention due to its enhancement of the complexity and controllability of chaotic maps, especially in the fields of secure communication and random number generation, which have shown promising applications. In this work, a three-dimensional discrete memristive hyperchaotic map (3D-DMCHM) based on cosine memristor is constructed. First, we analyze the fixed points of the map and their stability, showing that the map can either have a linear fixed point or none at all, and the stability depends on the parameters and initial state of the map. Then, phase diagrams, bifurcation diagrams, Lyapunov exponents, timing diagrams, and attractor basins are used to analyze the complex dynamical behaviors of the 3D-DMCHM, revealing that the 3D-DMCHM enters into a chaotic state through a period-doubling bifurcation path, and some special dynamical phenomena such as multi-layer differentiation, multi-amplitude control, and offset boosting behaviors are also observed. In particular, with the change of memristor initial conditions, there exists an offset that only homogeneous hidden chaotic attractors or a mixed state offset with coexistence of point attractors and chaotic attractors. Finally, we confirmed the high complexity of 3D-DMCHM through complexity tests and successfully implemented it using a digital signal processing circuit, demonstrating its hardware feasibility.

Spatiotemporal implicit neural representation as a generalized traffic data learner

Spatiotemporal Traffic Data (STTD) measures the complex dynamical behaviors of the multiscale transportation system. Existing methods aim to reconstruct STTD using low-dimensional models. However, they are limited to data-specific dimensions or source-dependent patterns, restricting them from unifying representations. Here, we present a novel paradigm to address the STTD learning problem by parameterizing STTD as an implicit neural representation. To discern the underlying dynamics in low-dimensional regimes, coordinate-based neural networks that can encode high-frequency structures are employed to directly map coordinates to traffic variables. To unravel the entangled spatial–temporal interactions, the variability is decomposed into separate processes. We further enable modeling in irregular spaces such as sensor graphs using spectral embedding. Through continuous representations, our approach enables the modeling of a variety of STTD with a unified input, thereby serving as a generalized learner of the underlying traffic dynamics. It is also shown that it can learn implicit low-rank priors and smoothness regularization from the data, making it versatile for learning different dominating data patterns. We validate its effectiveness through extensive experiments in real-world scenarios, showcasing applications from corridor to network scales. Empirical results not only indicate that our model has significant superiority over conventional low-rank models, but also highlight that the versatility of the approach extends to different data domains, output resolutions, and network topologies. Comprehensive model analyses provide further insight into the inductive bias of STTD. We anticipate that this pioneering modeling perspective could lay the foundation for universal representation of STTD in various real-world tasks. PyTorch implementations of this project is publicly available at:https://github.com/tongnie/traffic_dynamics.

Dynamic Analysis and FPGA Implementation of Fractional-Order Hopfield Networks with Memristive Synapse

Memristors have become important components in artificial synapses due to their ability to emulate the information transmission and memory functions of biological synapses. Unlike their biological counterparts, which adjust synaptic weights, memristor-based artificial synapses operate by altering conductance or resistance, making them useful for enhancing the processing capacity and storage capabilities of neural networks. When integrated into systems like Hopfield neural networks, memristors enable the study of complex dynamic behaviors, such as chaos and multistability. Moreover, fractional calculus is significant for their ability to model memory effects, enabling more accurate simulations of complex systems. Fractional-order Hopfield networks, in particular, exhibit chaotic and multistable behaviors not found in integer-order models. By combining memristors with fractional-order Hopfield neural networks, these systems offer the possibility of investigating different dynamic phenomena in artificial neural networks. This study investigates the dynamical behavior of a fractional-order Hopfield neural network (HNN) incorporating a memristor with a piecewise segment function in one of its synapses, highlighting the impact of fractional-order derivatives and memristive synapses on the stability, robustness, and dynamic complexity of the system. Using a network of four neurons as a case study, it is demonstrated that the memristive fractional-order HNN exhibits multistability, coexisting chaotic attractors, and coexisting limit cycles. Through spectral entropy analysis, the regions in the initial condition space that display varying degrees of complexity are mapped, highlighting those areas where the chaotic series approach a pseudo-random sequence of numbers. Finally, the proposed fractional-order memristive HNN is implemented on a Field-Programmable Gate Array (FPGA), demonstrating the feasibility of real-time hardware realization.

Analysis and evaluation of suitability of high-pressure dynamic constitutive model for concrete under blast and impact loading

Concrete demonstrates complex dynamic mechanical behaviors under the influence of blast or impact loads, and there are inherent limitations in experimental and theoretical methods when dealing with highly nonlinear problems. As computational technologies and mechanics continue to evolve, it is possible to conduct high-fidelity simulations of the transient response of concrete structures subjected to intense dynamic loads. Such simulations play a crucial role in revealing the propagation laws of stress waves, the progression of damage, the mechanisms of structural failure, and in conducting protective engineering design. An accurate concrete material model is essential for conducting numerical studies. This article reviews the development of high-pressure dynamic constitutive models for concrete in recent years from both experimental research and theoretical modeling perspectives, focusing on the analysis and evaluation of the modeling methods and main shortcomings of the equation of state(EOS), strength model, and damage model. Using single-element numerical simulations under a single loading path and numerical calculations of engineering cases under complex loading paths, a systematic analysis and comparison were conducted on the predictive capabilities of the HJC, RHT, KCC, and CSC models, as well as the newly developed Kong-Fang and Yan-Chen models. It pointed out the impact of high-pressure mechanical behavior of concrete and the cumulative effect of damage under hydrostatic pressure on the calculation results. Finally, a discussion was conducted on the inherent flaws, applicability, and research difficulties of local constitutive models of concrete in the finite element method. This provides a reference for the selection and research of constitutive models when conducting numerical analysis of the blast and impact resistance of concrete structures.

Insight into a new perspective on the complex propagation processes in networks: dynamic link equations

Insight into the spread of epidemics under different transmission mechanisms in networks has long been an important research question in the field of complex network dynamics. Currently, under simple transmission mechanisms, our analysis of the dynamic processes in networks starts only from the node level, considering the scale of infected nodes in the network. However, the information provided by this lowest-order approach to considering dynamic processes in networks is very limited. Most importantly, it is not applicable to the analysis of dynamic processes in networks under more common complex transmission mechanisms, as it neglects the interactions between nodes. Therefore, in this article, we propose a set of closed link dynamic equations to gain insight into complex propagation processes from a microscopic perspective. Fundamentally, we have developed a set of analytical tools for analyzing complex dynamic behaviors at the link level, enabling us to reexamine the complex dynamic processes on networks from a higher-order perspective. Additionally, we apply the proposed analytical framework to complex SIS epidemiological models on two real and synthetic networks, and extensive numerical simulation results demonstrate the feasibility and effectiveness of the proposed method.

Dynamic characteristics of shape-memory alloy plates immersed in liquid subjected to blast loading

As a critical structure in ship and marine engineering, axially moving shape-memory alloy (SMA) plates may exhibit complex dynamic behaviors. However, there are few studies investigating the dynamic response of SMA plates under underwater blast, let alone consider the effect of initial geometric imperfection and axial motion. Therefore, further studies on such topic are warranted. Based on this, the current paper dedicates to conducting the dynamic research of the geometrically imperfect SMA plate subjected to underwater blast. Firstly, adopting Falk's polynomial constitutive model, the stress strain constitutive relationship of SMA plate can be determined. Secondly, the Hamilton's principle is employed to derive the vibration equation. Thirdly, the assumed mode method and Runge-Kutta technique are applied for solving the dynamic system. After that, several comparative analyses are performed. Finally, the influences of immersed depth, axially moving velocity, initial geometric imperfection, elastic foundation, pulse load type, aspect ratio, length-to-thickness ratio, as well as blast loading parameter on the transient response path are discussed. These findings can contribute to understanding the dynamic behavior of the geometrically imperfect SMA plates immersed in water when subjected to blast loading, and thus providing valuable thinking for the manufacturing and design of submarine equipment.

Research on the complex dynamical behavior of H-bridge inverter with RLC load

Complex dynamical behaviors such as bifurcation and chaos exist in H-bridge inverter with RLC load, and these nonlinear behaviors will greatly increase the harmonic content of the output current and reduce the stability and reliability of the system. In this paper, a PI controller is added to widen the stable operation domain of the system. The stroboscopic mapping theory is used to model the system, the nonlinear dynamic behavior of the inverter is investigated by the bifurcation diagram, the folding diagram and the phase trajectory diagram are used for comparative verification, and the TDFC method is introduced to inhibit the chaotic behavior of the inverter, which further improves the stable range of the system operation. The fast-change stability theorem is used to analyze the stability of the system theoretically and verify the correctness of the numerical simulation. Therefore, the conclusions of the study provide a reliable theoretical basis for the design of the inverter system, which has important theoretical significance and practical value.

Propulsion and energy extraction performance of wave-powered mechanism considering wave and current

Wave-powered mechanism can extract wave energy as propulsion, enabling long-term ocean observation. The kinematic properties of wave propulsion mechanisms are susceptible to ocean current loads in addition to wave effects, presenting complex dynamic behaviors. In this paper, to understand the effects of ocean currents on the kinematic performances of wave propulsion mechanism, the dynamic performance of a wave propulsion mechanism in the combined condition of wave and current is analyzed based on numerical simulation method for fluid-rigid body coupling and experimental methods. The performance of the propulsion mechanism against the current under counter-current conditions and the contribution of flow to the propulsion performance under co-current conditions are discussed. The intrinsic relationship between wave height, current velocity and current direction is investigated, and the energy extraction performance of wave propulsion mechanism is analyzed. According to the results, the ability of propulsion mechanism to resist counter-current is obtained, and it is found that as the counter-current velocity increases, the hydrofoil will stall and the propulsion force and efficiency decreases significantly. Whilst, the co-current has a promoting effect on the forward of the mechanism, but within a certain range of co-current speed, the mechanism will be negatively affected by the shedding vortex. And the discrimination mechanisms for wave-dominated propulsion and current-dominated propulsion are obtained. This work reveals the combined effect of waves and currents on the motion performance of wave propulsion mechanism, providing a reference for the development of surface vehicles that utilize multiple ocean energies for synergistic propulsion.

Periodic and Quasi-Periodic Orbits in the Collinear Four-Body Problem: A Variational Analysis

This paper investigated the periodic and quasi-periodic orbits in the symmetric collinear four-body problem through a variational approach. We analyze the conditions under which homographic solutions minimize the action functional. We compute the minimal value of the action functional for these solutions and show that, for four equal masses organized in a linear configuration, these solutions are the minimizers of the action functional. Additionally, we employ numerical experiments using Poincaré sections to explore the existence and stability of periodic and quasi-periodic solutions within this dynamical system. Our results provide a deeper understanding of the variational principles in celestial mechanics and reveal complex dynamical behaviors, crucial for further studies in multi-body problems.

الصيغ التحليلية للاهتزازات المحورية والانحناء والقص والالتواء المقترنة لعوارض تيموشينكو ذات الصفائح المركبة الغير متماثلة

This paper presents the exact closed-form solutions for the vibration analysis of extension-bending-shear-torsion coupled responses in asymmetric laminated Timoshenko beams. The study derives four governing differential equations and corresponding boundary conditions using Hamilton’s variational principle. The formulation, based on first-order shear deformation theory (FSDT), accounts for rotary inertia, Poisson’s ratio, and extensional-flexural-torsional-shear coupling effects arising from material anisotropy. The exact solutions are obtained for various harmonic bending and twisting excitations under different boundary conditions, capturing the fully coupled axial, bending, and torsional responses. This approach offers a robust analytical method for understanding the complex dynamic behavior of laminated composite beams subjected to dynamic loads, with potential applications in aerospace, mechanical, and civil engineering structures, such as aircraft components, turbine blades, and bridges. Keywords: Closed-form solution; extension-bending-shear-torsion coupled response; harmonic excitations; asymmetric laminated beam.

COMPLEX DYNAMICAL BEHAVIORS OF A DISCRETE MODIFIED LESLIE–GOWER PREDATOR–PREY MODEL WITH PREY HARVESTING

Recently, the research on the modified Leslie–Gower model has become an appealing topic. Due to economic efficiency and the complexity of discrete models, we investigate a discrete modified Leslie–Gower predator–prey model with prey harvesting in this paper. The stability of fixed points and bifurcations of the interior fixed points are studied. According to bifurcation theory and normal forms, we derived the conditions of codimension 2 bifurcations occurred, including 1:1 strong resonance bifurcation and fold-flip bifurcation. These two bifurcations are unusual in bifurcation analysis on discrete systems. In addition, the continuation curves, bifurcation diagrams, and phase diagrams are used to demonstrate theoretical results. Our study shows the interesting dynamics of this model that are very different from the continuous one.