Nonlinear Discrete Systems Research Articles

SMETHODS FOR REDUCING THE PAPR OF FBMC SIGNALS BASED ON A DISCRETE-NONLINEAR SPROTT SYSTEM IMPLEMENTED OVER A FINITE GALOIS FIELD

In this article, we provide a comparative analysis of various methods for reducing the peak factor of Filter bank Multicarrier signals in a multiplexing system with a filter bank using the discrete-nonlinear Sprott system implemented over a finite Galois field. The methods of partial transmission sequence, scrambling, and a combined method, which includes both methods, are considered. Each method is based on the use of a pseudorandom sequence, the formation of which is provided by generators based on a discrete nonlinear Sprott system. As a result of the work, the peak factor for each method is estimated and an additional cumulative distribution function is also presented. In addition, the influence of the number of iterations and windows used in the partial transmission sequence method on the peak factor was estimated. The results obtained in the course of the study can be applied in the design of information transmission systems.

An energy stable finite element method for the nonlocal electron heat transport model

In this paper, the nonlocal electron heat transport model in one and two dimensions is considered and studied. An energy stability finite element method is designed to discretize the nonlocal electron heat transport model. For the nonlinear discrete system, both Newton iteration and implicit-explicit (IMEX) schemes are employed to solve it. Then the energy stability is proved in semi-discrete and fully-discrete schemes. Numerical examples are presented to verify the energy stability of the proposed schemes as well as the optimal convergence order in L∞, L2 and H1 norm.

Huygens synchronization of three aligned clocks

AbstractThis study examines the synchronization of three identical oscillators arranged in an array and coupled by small impacts, wherein each oscillator interacts solely with its nearest neighbour. The synchronized state, which is asymptotically stable, is characterized by phase opposition among alternating oscillators. We analyse the system using a non-linear discrete dynamical system based on a difference equation derived from the iteration of a plane diffeomorphism. We illustrate these results with the application to a system of three aligned Andronov clocks, showcasing their applicability to a broad range of oscillator systems.

Exponential admissibility and [formula omitted] control for nonlinear singular discrete systems with mixed time-varying delays

This study addresses the issue of exponential admissibility analysis and H∞ control for nonlinear singular discrete-time systems with mixed time-varying delays (NSDS-MTVD). By developing a set of improved Lyapunov-Krasovskii functionals, new delay-dependent criteria are constructed in terms of linear matrix inequalities (LMIs) to ensure the regularity, causality, and exponential admissibility with an H∞ performance level−γ of the NSDS-MTVD. Subsequently, the state feedback H∞ controller design approach is also presented as an application of the obtained result. In the case of a linear singular system, corresponding corollaries is derived. Numerical examples are provided to demonstrate the effectiveness of the acquired results.

Assessing Stability in Discrete-Time Systems Impacted by Interference and State Delays: An Approach Using ISS

In this study, we introduce a criterion for addressing the input to state stability (ISS) problem inherent in nonlinear discrete systems featuring state delay, saturation overflow (SO), and external interference (EI). This paper proposes three novel theorems by employing the Lyapunov function to assure the stability of the targeted discrete time systems (DTS) under complex conditions such as state delay, SO, EI and the first theorem utilizes system information more effectively by considering EI, state delay and SO, the second theorem focuses on asymptotic stability (AS) analysis of the system when EIs are zero, the third theorem proposes the system is AS when state delays are zero. These theorems impose fewer constrains additionally these conditions are demonstrated to be more relaxed and computationally less intensive to existing criteria. The advantage of the suggested technique is proven through three numerical examples and comparison research.

Asymptotic behavior of solutions of nonlinear discrete systems in critical cases

The paper is dedicated to the analysis of the asymptotic behavior of essentially nonlinear discrete systems whose linearization possesses eigenvalues on the unit circle. For these systems, the paper establishes sufficient conditions for the asymptotic stability regardless of terms higher than the third order. Moreover, it derives an asymptotic stability criterium for a reduced critical subsystem. The proof incorporates a constructive approach for deriving Lyapunov functions using the center manifold reduction and normal form method. The key result of the paper asserts that, given the obtained stability conditions, the solutions of the system converge to the origin with a polynomial decay rate. The paper also introduces a method for evaluating the coefficients of the decay rate estimate. To illustrate these findings, we apply the obtained result to analyzing nonlinear business cycle and predator-pray models.

Estimation of probabilities of transitions of markov binary input signal of nonlinear system

The problem of estimating unknown probabilities of transitions of a random Markov binary input signal of a nonlinear one-dimensional discrete system based on estimating the expectation and variance of the output signal is considered. The defined expressions are built on the basis of considering equally probable transitions and the steady-state mode of the algorithm for assessing the state of the system, obtained by approximating the probability density of its output signal by the Pearson type I distribution. An example of comparison of theoretical calculations with the results of imitation mathematical modeling is given.

The Dynamic Event-Based Non-Fragile H∞ State Estimation for Discrete Nonlinear Systems with Dynamical Bias and Fading Measurement

The present study investigates non-fragile H∞ state estimation based on a dynamic event-triggered mechanism for a class of discrete time-varying nonlinear systems subject to dynamical bias and fading measurements. The dynamic deviation caused by unknown inputs is represented by a dynamic equation with bounded noise. Subsequently, the augmentation technique is employed and the dynamic event-triggered mechanism is introduced in the sensor-to-estimator channel to determine whether data should be transmitted or not, thereby conserving resources. Furthermore, an augmented state-dependent non-fragile state estimator is constructed considering gain perturbation of the estimator and fading measurements during network transmission. Sufficient conditions are provided based on Lyapunov stability and matrix analysis techniques to ensure exponential mean-square stability of the estimation error system while satisfying the H∞ disturbance fading level. The desired estimator gain matrix can be obtained by solving the linear matrix inequality (LMI). Finally, an example is presented to illustrate the effectiveness of the proposed method for designing estimators.

A novel intelligent control of discrete-time nonlinear systems in the presence of output saturation

In this paper, a model free control method for a class of discrete time nonlinear systems is introduced. A type-3 fuzzy system estimates the unknown parameters required by the control system. The control system only uses the input and output data of the plant and therefore does not need to know its mathematical equations. On the other hand, the phenomenon of output saturation is a challenging problem for all control systems, addressed in detail in the proposed method. The convergence of the proposed method is guaranteed, and the control system is very robust in the face of changes in the dynamics of the plant. The simulation results on discrete-time nonlinear systems show that the proposed method is very accurate despite the high speed of convergence. In addition, the proposed method is robust for modeling uncertainties and has a better root mean square error and step response time compared to the other methods. Also, a comparison has been made between type-1 to type-3 fuzzy systems and control system based on trial and error, which shows firstly the importance of the presence of fuzzy system and secondly the superiority of type-3 fuzzy system compared to the other two types.

Adaptive learning control for group consensus tracking of discrete nonlinear multiagent systems

Adaptive learning control for group consensus tracking of discrete nonlinear multiagent systems

Numerical simulations of energy storage performance in a close configuration: A Galerkin finite element-based computation

The energy storage features on natural convection in Casson fluids are investigated in this work using the finite element method. By measuring cylinders and wavy surfaces, we may examine flow patterns and the effectiveness of heat transmission systems. We study the variation of the mass and heat transfer rates as a function of the cylinder geometry. To approximately determine velocities and temperatures, the Ladyzhenskaya-Babuška—Brezzi (LBB)-stable element is employed. Following this discretization, the resulting discrete nonlinear system is linearized using Newton's method and subsequently solved using PARDISO. Fractional applications in Casson fluid analysis reveal insights into energy storage effects, employing finite element methods to explore flow patterns, heat transmission efficiency, and geometric variations while observing the impact of parameters such as Rayleigh, Hartmann, and Lewis numbers on fluid behavior and thermal properties. The preceding research has verified the accuracy of the numerical results. According to the results, concentration gradients and other modifications to liquids become more noticeable as the Rayleigh number grows. Convective heat transmission is reduced as the Ha is raised. When the Le grows, the deformation Nuavg and Shavgalso increase. Reducing the beta makes the isotherms more stable and less affected by the motion of the fluid.

Highly accurate wavelet solution for the two-dimensional Bratu's problem

A modified wavelet interpolation Galerkin method (WIGM) with improved flexibility of nodal distribution is formulated and utilized to solve the Bratu's problem. Such a method treats the nonlinear term as an independent function and directly approximates it through the proposed wavelet interpolation, resulting in a low-cost discretization of the Bratu's equation with exponential nonlinearity. An efficient implementation of Newton's method to find the lower and upper branches of solution as well as the turning point is then presented. Numerical results demonstrate that the present WIGM can accurately estimate both two solution branches and turning point for the Bratu's problem. Compared with many other existing methods, the proposed WIGM also offers marked superiority in terms of accuracy when using the same node distribution. Moreover, a convergent solution to the resulting nonlinear discrete system obtained by the WIGM can be observed in a few iterations even when the initial guess significantly deviates from the exact solution. Finally, a highly accurate approximation of both two-branched solutions and the turning point for the two-dimensional Bratu's problem is obtained by the proposed WIGM.

Aperiodic intermittent sampling for nonlinear discrete-time event-based model predictive control

ABSTRACT In this article, an aperiodic intermittent sampling method is designed in event-based model predictive control for nonlinear discrete systems subject to external disturbances. The proposed aperiodic intermittent sampling is applied to find the appropriate triggering instant satisfying the desired sub-optimal performance. In the proposed event-based MPC, selection of the sampling instants is based on the prediction of the worst case induced by disturbances and the mapping principle with updated state feedback. With the proposed event-based MPC, the measurement frequency and the triggering rate can be reduced by sampling the system states only at certain time instants. Recursive feasibility and robust stability are established under sufficient conditions.

Enhanced parallel computation for time-fractional fluid dynamics: A fast time-stepping method with Newton-Krylov-Schwarz solver

This paper presents a sum-of-exponentials domain decomposition method for the numerical simulation of two-dimensional unsteady fluid flow and heat transfer using a time-fractional fluid model. We employ a fast time-stepping approach to discretize the time-fractional derivatives, followed by the application of a parallel Newton-Krylov-Schwarz algorithm to solve the resulting discrete nonlinear system. The numerical experiments demonstrate a superior performance of the fast time-stepping method compared to the traditional L1 scheme, particularly in the context of parallel computation, as it substantially reduces the computational complexity and memory usage. The algorithm exhibits robust performance across a wide range of model parameters and solver settings. Notably, it achieves 60% parallel efficiency with the use of 768 processor cores. This study underscores the efficacy of parallel processing as a potent computational strategy for addressing the challenges in solving time-fractional partial differential equations.

Nonlinear causal network learning via Granger causality based on extreme support vector regression.

For complex networked systems, based on the consideration of nonlinearity and causality, a novel general method of nonlinear causal network learning, termed extreme support vector regression Granger causality (ESVRGC), is proposed. The nonuniform time-delayed influence of the driving nodes on the target node is particularly considered. Then, the restricted model and the unrestricted model of Granger causality are, respectively, formulated based on extreme support vector regression, which uses the selected time-delayed components of system variables as the inputs of kernel functions. The nonlinear conditional Granger causality index is finally calculated to confirm the strength of a causal interaction. Generally, based on the simulation of a nonlinear vector autoregressive model and nonlinear discrete time-delayed dynamic systems, ESVRGC demonstrates better performance than other popular methods. Also, the validity and robustness of ESVRGC are also verified by the different cases of network types, sample sizes, noise intensities, and coupling strengths. Finally, the superiority of ESVRGC is successful verified by the experimental study on real benchmark datasets.

On–Off Intermittency and Long-Term Reactivity in a Host–Parasitoid Model with a Deterministic Driver

Bursting behaviors, driven by environmental variability, can substantially influence ecosystem services and functions and have the potential to cause abrupt population breakouts in host–parasitoid systems. We explore the impact of environment on the host–parasitoid interaction by investigating separately the effect of grazing-dependent habitat variation on the host density and the effect of environmental fluctuations on the average host population growth rate. We hence focus on the discrete host–parasitoid Beddington–Free–Lawton model and show that a more comprehensive mathematical study of the dynamics behind the onset of on–off intermittency in host–parasitoid systems may be achieved by considering a deterministic, chaotic system that represents the dynamics of the environment. To this aim, some of the key model parameters are allowed to vary in time according to an evolution law that can exhibit chaotic behavior. Fixed points and stability properties of the resulting 3D nonlinear discrete dynamical system are investigated and on–off intermittency is found to emerge strictly above the blowout bifurcation threshold. We show, however, that, in some cases, this phenomenon can also emerge in the sub-threshold. We hence introduce the novel concept of long-term reactivity and show that it can be considered as a necessary condition for the onset of on–off intermittency. Investigations in the time-dependent regimes and kurtosis maps are provided to support the above results. Our study also suggests how important it is to carefully monitor environmental variability caused by random fluctuations in natural factors or by anthropogenic disturbances in order to minimize its effects on throphic interactions and protect the potential function of parasitoids as biological control agents.

High Efficiency Data Driven Control Based on Dynamic Linearization and PIDNN With Cohen-Coon for Discrete Nonlinear Fast Time-Varying Systems

High Efficiency Data Driven Control Based on Dynamic Linearization and PIDNN With Cohen-Coon for Discrete Nonlinear Fast Time-Varying Systems

Complex dynamics of a nonlinear discrete predator-prey system with Allee effect

Complex dynamics of a nonlinear discrete predator-prey system with Allee effect

Design of Functional Interval Observer for Discrete Time-Varying Nonlinear Interconnected Systems Based on Coding-Decoding Scheme

In this paper, we design a distributed functional interval observer for discrete time-varying nonlinear interconnected systems. The communication between subsystems adapts the coding-decoding scheme (CDS) to save bandwidth and avoid data conflicts. The state set is described by the ellipsoid which can improve estimation accuracy and reduce conservatism. Besides, we give the conditions for the establishment of the observer and the stability of the error dynamic system. The observer gain matrices are obtained by solving a set of linear matrix inequalities (LMI) and some given conditions. The shape matrix of the ellipsoid is determined by selecting the optimal solution. Finally, we give two simulation examples to prove the designed functional interval observer is effective.

Robust Control of Nonlinear Discrete Systems With Perturbations Based on Estimated State Feedback

Robust Control of Nonlinear Discrete Systems With Perturbations Based on Estimated State Feedback