Complex Dynamic Behavior Research Articles

Stochastic analysis of combined primary-secondary structures subjected to imprecise seismic excitation

The imprecise stochastic process model is able to incorporate both random and epistemic uncertainties, leading to a more accurate description of environmental excitations, such as earthquakes or wind loads, when limited data are available. Epistemic uncertainties in the loading model may significantly affect the performance of structural systems.The present paper addresses the stochastic analysis of combined primary-secondary structures subjected to imprecise seismic excitation modeled as a zero-mean stationary Gaussian random process, characterized by an interval-valued Power Spectral Density (PSD) function. The power and energy content of the imprecise ground motion acceleration may vary, even for the same soil category, affecting the complex dynamic behavior of combined structures and the vibration control capacity of secondary substructures under different frequency tuning conditions. The main purpose of this study is to develop a framework for investigating both the influence of epistemic uncertainties in the loading model and the interaction effects between the subsystems on the seismic performance of combined primary-secondary structures. To this aim, the stochastic analysis of combined structures under imprecise ground motion acceleration is addressed in both the frequency and time domains by an efficient approach capable of decoupling the propagation of interval and random uncertainties. Seismic safety assessment is performed in the framework of the first-passage theory by interval extension.

AI-Lorenz: A physics-data-driven framework for Black-Box and Gray-Box identification of chaotic systems with symbolic regression

Discovering mathematical models that characterize the observed behavior of dynamical systems remains a major challenge, especially for systems in a chaotic regime, due to their sensitive dependence on initial conditions and the complex non-linear interactions within the system. The challenge is even greater when the physics underlying such systems is not yet understood, and scientific inquiry must solely rely on empirical data. Despite advancements such as the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm, which has shown success in identifying chaotic systems with reasonable accuracy, challenges remain in dealing with noise, sparse data, and the need for models that generalize well across different chaotic systems. Driven by the need to fill this gap, we develop a framework named AI-Lorenz that learns mathematical expressions modeling complex dynamical behaviors by identifying differential equations from noisy and sparse observable data. We train a physics-informed neural network (PINN) with the eXtreme Theory of Functional Connections (X-TFC) algorithm by using data and known physics (when available) to learn the dynamics of a system, its rate of change in time, and missing model terms, which are used as input for a symbolic regression algorithm (PySR) to autonomously distill the explicit mathematical terms. This, in turn, enables us to predict the future evolution of the dynamical behavior. The performance of this framework is validated by recovering the right-hand sides and unknown terms of certain complex, chaotic systems, such as the well-known Lorenz system, a six-dimensional hyperchaotic system, the non-autonomous Sprott chaotic system, and the slow-fast Duffing system, and comparing them with their known analytical expressions and state-of-the-art regression and system identification methods.

A model of dyadic merging interactions explains human drivers' behavior from control inputs to decisions.

Safe and socially acceptable interactions with human-driven vehicles are a major challenge in automated driving. A good understanding of the underlying principles of such traffic interactions could help address this challenge. Particularly, accurate driver models could be used to inform automated vehicles in interactions. These interactions entail complex dynamic joint behaviors composed of individual driver contributions in terms of high-level decisions, safety margins, and low-level control inputs. Existing driver models typically focus on one of these aspects, limiting our understanding of the underlying principles of traffic interactions. Here, we present a Communication-Enabled Interaction model based on risk perception, that does not assume humans are rational and explicitly accounts for communication between drivers. Our model can explain and reproduce observed human interactions in a simplified merging scenario on all three levels. Thereby improving our understanding of the underlying mechanisms of human traffic interactions and posing a step towards interaction-aware automated driving.

Spatiotemporal complexity analysis of a discrete space-time cancer growth model with self-diffusion and cross-diffusion

We investigate spatiotemporal pattern formation in cancer growth using discrete time and space variables. We first introduce the coupled map lattices (CMLs) model and provide a dynamical analysis of its fixed points along with stability results. We then offer parameter criteria for flip, Neimark–Sacker, and Turing bifurcations. In the presence of spatial diffusion, we find that stable homogeneous solutions can experience Turing instability under certain conditions. Numerical simulations reveal a variety of spatiotemporal patterns, including patches, spirals, and numerous other regular and irregular patterns. Compared to previous literature, our discrete model captures more complex and richer nonlinear dynamical behaviors, providing new insights into the formation of complex patterns in spatially extended discrete tumor models. These findings demonstrate the model’s ability to capture complex dynamics and offer valuable insights for understanding and treating cancer growth, highlighting its potential applications in biomedical research.

Mobile Robot Motion Behavior Based on Hopfield Neural Network Dynamics Under Electromagnetic Radiation

The nonlinear characteristic of activation function is a critical aspect that affects the performance of artificial neural networks (ANNs). Despite its importance, the impact of neuronal nonlinearity variations on the dynamics of ANNs has not been thoroughly studied in previous research. This paper aims to fill this gap by exploring the influence of nonlinearity changes in activation function due to memristive electromagnetic induction on the dynamical characteristics of ANNs. We first propose a memristor model with sinusoidal conductance function. Then, the effects on the biological neuron under the electromagnetic induction are simulated by replacing the gradient of hyperbolic tangent activation function with the conductance of the proposed memristor. Furthermore, a Hopfield neural network (HNN) is constructed by taking the nonlinearity changes of activation function into consideration and its dynamical behaviors are analyzed through Lyapunov exponent spectra, bifurcation diagram, biparameter-based dynamic maps and phase portraits. The numerical simulation results show complex dynamical behaviors such as single-scroll chaotic spiral attractor, double-scroll chaotic attractors and initial-value-dependent offset boosted attractors, demonstrating that nonlinearity changes of activation function induced by the electromagnetic induction have a significant impact on the dynamics of HNN. To further verify our findings, we implement the proposed HNN in hardware and find that the results are in line with our numerical simulations. Finally, we apply the chaotic HNN in the mobile robot path planning task, which achieves higher coverage rate than the random number-based random walk method.

Design and FPGA implementation of nested grid multi-scroll chaotic system

Conventional multi-scroll chaotic systems are often constrained by the number of attractors and the complexity of generation, making it challenging to meet the increasing demands of communication and computation. This paper revolves around the modified Chua’s system. By modifying its differential equation and introducing traditional nonlinear functions, such as the step function sequence and sawtooth function sequence. A nested grid multi-scroll chaotic system (NGMSCS) can be established, capable of generating nested grid multi-scroll attractors. In contrast to conventional grid multi-scroll chaotic attractors, scroll-like phenomena can be initiated outside the grid structure, thereby revealing more complex dynamic behavior and topological features. Through the theoretical design and analysis of the equilibrium point of the system and its stability, the number of saddle-focused equilibrium points of index 2 is further expanded, which can generate (2 N+2) × M attractors, and the formation mechanism is elaborated and verified in detail. In addition, the generation of an arbitrary number of equilibrium points in the y-direction is achieved by transforming the x and y variables, which can generate M×(2 N+2) attractors, increasing the complexity of the system. The system’s dynamical properties are discussed in depth via time series plots, Lyapunov exponents, Poincaré cross sections, 0–1 tests, bifurcation diagrams, and attraction basins. The existence of attractors is confirmed through numerical simulations and FPGA-based hardware experiments.

Peridynamics modelling of projectile penetration into concrete targets

A non-ordinary state-based peridynamics (NOSB-PD) model is proposed to simulate the projectile penetration into concrete targets. In this model, the Kong-Fang concrete material model recently proposed is firstly implemented into the NOSB-PD framework to describe the complex dynamic behavior and failures in concrete material subjected to penetration loading, and then an improved point-to-volume discrete frictional contact model is proposed to simulate the physical interaction between projectile and target. After the mesh-free discretization and explicit time integration, the proposed NOSB-PD model is used to numerically predict two sets of projectile penetration experiments into low-strength and high-strength concrete targets. And numerical predictions are found to be in good agreements with corresponding test data including penetration depth, projectile deceleration, deformation of projectile and failures in concrete targets.

Dynamics analysis and FPGA implementation of discrete memristive cellular neural network with heterogeneous activation functions

The activation function, as an important component of artificial neural networks, endows neural networks with rich dynamical phenomena by virtue of its nonlinear properties. However, especially for cellular neural networks (CNNs), the exploration of neural networks consisting of heterogeneous activation functions has not been sufficient. In this article, we introduce heterogeneous activation functions in discrete cellular neural network (DCNN) for the first time. In order to enhance the dynamics of the original DCNN, we propose our discrete memristive cellular neural network (DMCNN) based on a memristor with a sinusoidal function. Using various methods of dynamical characterization, such as Lyapunov exponential analysis, bifurcation diagrams and spectral entropy, the rich dynamical behaviour of the proposed model is comprehensively investigated, including hyperchaos, transient chaos, high spectral entropy and multiple types of coexisting attractors in the proposed model. Last but not least, the hardware platform of the proposed model is implemented by field programmable gate array (FPGA), and the dynamics of the proposed model is verified by a combination of software simulation and hardware experiments. The new exploration of DMCNN with heterogeneous activation functions in this article lays the foundation for further research into neural networks with complex dynamical behaviour.

Function matrix projective synchronization for disturbed fractional laser chaotic systems and image encryption

Fractional laser chaotic systems can exhibit more complex dynamical behavior, so its projective synchronization and applications to image encryption have been widely investigated in recent years. This work devotes to realize its function matrix projective synchronization, whose projective scale factor is a function matrix varying with time t, and applies the function matrix projective synchronization to the color image encryption. First, two different fractional laser chaotic systems with model uncertainty and external disturbance are constructed and the function matrix projective synchronization is defined. Second, the fractional sliding mode surface and the sliding mode controller are designed to achieve the function matrix projective synchronization. And, the synchronization analysis is confirmed by numerical simulation. Finally, by Zigzag transformation and DNA coding, the function matrix projective synchronization is applied to the color image encryption. And the comparison results shows that an excellent encryption scheme can be designed by the complex projection factor. This work not only extends the concept of the projective synchronization, but also provides an effective method for the image encryption.

Memristors-coupled neuron models with multiple firing patterns and homogeneous and heterogeneous multistability

Abstract Memristors are extensively used to estimate the external electromagnetic stimulation and synapses for neurons. In this paper, two distinct scenarios, i.e., an ideal memristor serves as external electromagnetic stimulation and a locally active memristor serves as a synapse, are formulated to investigate the impact of a memristor on a two-dimensional Hindmarsh–Rose neuron model. Numerical simulations show that the neuronal models in different scenarios have multiple burst firing patterns. The introduction of the memristor makes the neuronal model exhibit complex dynamical behaviors. Finally, the simulation circuit and DSP hardware implementation results validate the physical mechanism, as well as the reliability of the biological neuron model.

Mechanical modeling and parameter analysis of the docking process for probe-drogue docking mechanisms

The on-orbit probe-drogue berthing docking of two spacecraft can effectively reduce impact force and adjust for initial deviations. However, its dynamic response and influence behaviors of design parameters are extremely concerning but difficult to obtain because of its complicated structure. In this paper, a fast mechanical modeling (FMM) method is proposed to obtain the dynamic response of probe-drogue docking mechanisms during spacecraft berthing missions. Regarding the quasi-static docking process, complex dynamic docking behaviors are simplified and decoupled. The FMM method divides docking into three contact processes based on the scene of contact; it analyzes the deviation adaptive docking principle of this type of docking mechanism by establishing the kinematics and mechanics models of active and passive parts. The finite element simulations and experiments of probe-drogue berthing docking were used to compare with the proposed FMM. The comparison results of different initial deviation conditions indicate that the FMM method guarantees computation accuracy and increases computation speed by two orders of magnitude, which greatly reduces computation costs. Then this efficient FMM method was utilized to analyze the influence of key parameters, such as friction coefficient and cone angle, on the contact force and driving force of the docking mechanism. The conclusions of the parameter analysis of probe-drogue berthing docking can be used to reduce contact force and accelerate iterative design as a reference for the design of this kind of docking mechanisms, making the docking process optimized and reliable.

Global dynamic analyzes of the discrete SIS models with application to daily reported cases

Emerging infectious diseases, such as COVID-19, manifest in outbreaks of varying magnitudes. For large-scale epidemics, continuous models are often employed for forecasting, while discrete models are preferred for smaller outbreaks. We propose a discrete susceptible-infected-susceptible model that integrates interaction between parasitism and hosts, as well as saturation recovery mechanisms, and undertake a thorough theoretical and numerical exploration of this model. Theoretically, the model incorporating nonlinear recovery demonstrates complex behavior, including backward bifurcations and the coexistence of dual equilibria. And the sufficient conditions that guarantee the global asymptotic stability of a disease-free equilibrium have been obtained. Considering the challenges posed by saturation recovery in theoretical analysis, we then consider the case of linear recovery. Bifurcation analysis for of the linear recovery model displays a variety of bifurcations at the endemic equilibrium, such as transcritical, flip, and Neimark–Sacker bifurcations. Numerical simulations reveal complex dynamic behavior, including backward and fold bifurcations, periodic windows, period-doubling cascades, and multistability. Moreover, the proposed model could be used to fit the daily COVID-19 reported cases for various regions, not only revealing the significant advantages of discrete models in fitting, evaluating, and predicting small-scale epidemics, but also playing an important role in evaluating the effectiveness of prevention and control strategies. Furthermore, sensitivity analyses for the key parameters underscore their significant impact on the effective reproduction number during the initial months of an outbreak, advocating for better medical resource allocation and the enforcement of social distancing measures to curb disease transmission.

Dynamics Modeling and Analysis of Small-Diameter Pipeline Inspection Gauge during Passing Through Elbow

Abstract With small diameters, numerous elbows and complex internal environment, gathering and transportation pipelines are widely applied in the oil and gas pipeline network. To guarantee their safety, a pipeline inspection gauge (PIG) driven by the pressure differential is used. When the PIG collides with the elbows in the pipeline, it exhibits complex nonlinear dynamic behaviors and its reliability and stability may also be greatly affected. To study the vibration response characteristics passing through the elbow, the dynamic modeling of the small-diameter PIG is conducted first in this paper based on the ADAMS software. Then, the fluid-structure coupling is achieved by combining the dynamic model and the numerical calculation program of the fluid equation in Simulink. The simulation results indicate that the axial and swing acceleration amplitudes of the two sections increase with the increasing speed of the double-section detector, while the opposite trend is observed for the vertical acceleration amplitudes. By comparison, it is found that the acceleration response in the second section is generally greater than that in the first section. The results also show that the axial offset of the PIG at the elbow is inversely proportional to the speed and radius of the elbow, which is the main cause of the lift-off values of sensors.

Image encryption algorithm based on DNA mutation and a novel four-dimensional hyperchaos

Abstract Aiming at the problem that insufficient complexity of ordinary multi-dimensional chaotic systems and the cumbersome design of encryption algorithms without excellent encryption effects. This paper constructs a four-dimensional hyperchaotic system with high Lyapunov exponent and complex dynamic behavior. We designed an encryption algorithm based on point mutation, mutation diffusion, and folding mutation in DNA mutations. During the encryption process, we perform point mutation transformation on the entire base sequence, then spread the mutations one by one starting from the second base of the sequence, and finally flip every four base sequences according to folding mutations. The images encrypted by this algorithm have a uniform grayscale histogram, high information entropy, and high key sensitivity. It can resist exhaustive attacks, noise attacks, cropping attacks, and differential attacks, and have a fast encryption speed.

Complex dynamical properties and chaos control for a discrete modified Leslie-Gower prey-predator system with Holling II functional response

In this study, the semi-discretization technique is employed to establish a discrete representation of a modified Leslie-Gower prey-predator system that includes a Holling II type functional response. The dynamics of this model are then analyzed through the application of center manifold theory and bifurcation theory. We present comprehensive results for the local stability of the fixed points across the entire parameter space. Additionally, we provide sufficient conditions for the occurrence of flip bifurcation and Neimark-Sacker bifurcation. Besides, the system has experienced a flip bifurcation to chaos controlled using the method of chaos control, viz., state feedback method, pole placement technique, and hybrid control strategy. Furthermore, we provide specific conditions to ensure that bifurcation and chaos can be stabilized. Finally, numerical simulations are conducted to validate theoretical analysis and illustrate several new complex dynamical behaviors between two species.

Complex dynamics in nonlinear small time-delayed optoelectronic oscillator and application in fast reservoir computing and pulse generation

We investigated a time-delayed optoelectronic oscillator (OEO) that displays a wide range of complex dynamic behavior under small time delay. The phase-space trajectory distributions in different dynamic regimes were compared which brings a new perspective on the underlying mechanism of the transition process. It was found that bifurcation is always possible no matter how small the time delay is even if the universal adiabatic approximation model is invalid. Hereby we proposed a versatile simple oscillator which has a potential capacity as memory carrier and high-dimensional state spatial mapping ability that brings 1000 times computing-efficiency improvements of reservoir computing over the large time delay one. Furthermore, we demonstrated a new approach for a tunable optoelectronic pulse generator (repetition rate at 0.2 MHz and 0.25 GHz) which depends critically on time-delayed input electrical pulse. The proposed oscillator is also a promising system for the applications of fast chaos-based communication.

Characteristic value decomposition: A unifying paradigm for data-driven modal analysis

Data-driven modal analysis is an indispensable means to understand the dynamic behavior of engineered structures and natural systems. It effectively captures active dynamic behavior and embeds them in a set of identified linear modal subspaces, unveiling complex dynamic behavior via the superposition of simpler hierarchical spatiotemporal dynamics. Despite the existence of many methods, there is no unified perspective connecting these modal analysis techniques. This paper proposes a new modal decomposition method, the characteristic value decomposition (CVD), that provides a unifying paradigm for data-driven modal analysis. CVD identifies identical spatial modes and temporal coordinates from two measurement data matrices. The modal parameters are identified through an eigendecomposition to a quotient of auto-covariance and cross-covariance matrices of the two data matrices. This paper shows that several data-driven modal analysis methods, namely, the state-variable decomposition, the dynamic mode decomposition, the Ibrahim time domain method, and the eigensystem realization algorithm, are special cases of CVD when the two data matrices are appropriately selected. Moreover, the CVD identifies the modal parameters with higher accuracy and is robust to added noise compared to established methods, as demonstrated using numerical experiments. It is also shown that the CVD flexibly utilizes data from multiple experiments and undersampled data sets to unveil system dynamics.

Dynamic behaviors of far and near memristive electromagnetic induction in spoon neural network.

In this paper, a special spoon neural network is proposed, which is composed of four neurons with direct connection and indirect connection. On this basis, the far induction network and the near induction network (NINN) are constructed by using hyperbolic tangent memristors to explore the influence of electromagnetic induction between neurons at different positions on the dynamic behavior of attractors. NINN exhibits more complex attractor structures and wider chaotic parameters, and also displays a heterogeneous coexisting attractor of limit cycles and chaos under network parameter control. By varying the parameters, coexisting chaotic attractors can be synthesized into a double scrolls attractor, and their oscillation amplitude can be controlled without changing the chaotic characteristics. The type of attractors in human brain determines the clarity of memory. These complex dynamic behaviors demonstrate that near induction has a more pronounced effect on the forgetting and disappearance of memory compared to far induction. Finally, a circuit using switches to change the type of electromagnetic induction is constructed and the results are verified.

Dynamical analysis of a novel 2D Lyapunov exponent controllable memristive chaotic map.

The proposal of discrete memristors has made memristive chaotic maps based on them an important research topic. In this study, a new two-dimensional chaotic map without fixed points is constructed, and numerical simulation results display its rich dynamical behaviors. The analysis reveals the map's center inversion symmetry and Lyapunov exponent controller. The map exhibits complex dynamical behaviors, including memristor initial-boosting and single-parameter-offset boosting. Embedding the absolute value function within the memristor results in the emergence of localized boosting-free regions. Moreover, a class of multicavity transients is captured that greatly enhances the system's complexity. Ultimately, this map is implemented on the STM32 platform, demonstrating its practical applicability in potential practical application scenarios.

Unified understanding of the impact of semiflexibility, concentration, and molecular weight on macromolecular-scale ring diffusion

Conformationally fluctuating, globally compact macromolecules such as polymeric rings, single-chain nanoparticles, microgels, and many-arm stars display complex dynamic behaviors due to their rich topological structure and intermolecular organization. Synthetic rings are hybrid objects with conformations that display both ideal random walk and compact globular features, which can serve as models of genomic DNA. To date, emphasis has been placed on the effect of ring molecular weight on their unusual behaviors. Here, we combine simulations and a microscopic force-level theory to build a unified understanding for how key aspects of ring dynamics depend on different tunable molecular properties including backbone rigidity, monomer concentration, degree of traditional entanglement, and molecular weight. Our large-scale molecular dynamics simulations of ring melts with very different backbone stiffnesses reveal unanticipated behaviors which agree well with our generalized theory. This includes a universal master curve for center-of-mass diffusion constants as a function of molecular weight scaled by a chemistry and thermodynamic state-dependent critical molecular weight that generalizes the concept of an entanglement cross-over for linear chains. The key physics is how backbone rigidity and monomer concentration induced changes of the entanglement length, interring packing, degree of interpenetration, and liquid compressibility slow down space-time dynamic-force correlations on macromolecular scales. A power law decay of the center-of-mass diffusion constant with inverse molecular weight squared is the first consequence, followed by an ultraslow activated hopping transport regime. Our results set the stage to address slow dynamics and kinetic arrest in different families of compact synthetic and biological polymeric systems.