Coexisting multi-stable patterns in memristor synapse-coupled Hopfield neural network with two neurons

Nonlinear Dynamics - When possessing a potential difference between two neurons, an electromagnetic induction current appears in the Hopfield neural network (HNN), which can be emulated by a...     

Robust sensor fault estimation for fractional-order systems with monotone nonlinearities

Nonlinear Dynamics - This paper investigates the problem of sensor fault estimation for systems with monotone nonlinearities and unknown inputs. To the best of our knowledge, such a particular...     

Variational parameter estimation for a two-dimensional numerical tidal model

It is shown that the parameters in a two-dimensional (depth-averaged) numerical tidal model can be estimated accurately by assimilation of data from tide gauges. The tidal model considered is a semi-linearized one in which kinematical non-linearities are neglected but non-linear bottom friction is included. The parameters to be estimated (bottom friction coefficient and water depth) are assumed to be position-dependent and are approximated by piecewise linear interpolations between certain nodal values. The numerical scheme consists of a two-level leapfrog method. The adjoint scheme is constructed on the assumption that a certain norm of the difference between computed and observed elevations at the tide gauges should be minimized. It is shown that a satisfactory numerical minimization can be completed using either the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton algorithm or Nash's truncated Newton algorithm. On the basis of a number of test problems, it is shown that very effective estimation of the nodal values of the parameters can be achieved provided the number of data stations is sufficiently large in relation to the number of nodes.     

Chaos detection and parameter identification in fractional-order chaotic systems with delay

The paper first applies the 0–1 test for chaos to detecting chaos exhibited by fractional-order delayed systems. The results of the test reveal that there exists chaos in some fractional-order delayed systems with specific parameter values, which coincides with previous reports based on the phase portrait. In addition, it is very important to identify exactly the unknown specific parameters of fractional-order chaotic delayed systems in chaos control and synchronization. Thus, a method for parameter identification of fractional-order chaotic delayed systems based on particle swarm optimization (PSO) is presented. By treating the orders as parameters, the parameters and orders are identified through minimizing an objective function. PSO can efficiently find the optimal feasible solution of the objective function. Finally, numerical simulations on fractional-order chaotic logistic delayed system and fractional-order chaotic Chen delayed system show that the proposed method has effective performance of parameter identification.     

Gradient-based parameter estimation for input nonlinear systems with ARMA noises based on the auxiliary model

This paper presents a gradient-based iterative identification algorithm and an auxiliary-model-based multi-innovation generalized extended stochastic gradient algorithm for input nonlinear systems with autoregressive moving average (ARMA) noises, i.e., the input nonlinear Box–Jenkins (IN–BJ) systems. The estimation errors given by the gradient-based iterative algorithm are smaller than the generalized extended stochastic gradient algorithm under same data lengths. A simulation example is provided.     

Bifurcation control for a fractional-order competition model of Internet with delays

Nonlinear Dynamics - In today’s society, the Internet has become an important tool of our life due to its potential applications in various areas such as economics, industry, agriculture,...     

A simulated annealing-based inverse computational fluid dynamics model for unknown parameter estimation in fluid flow problem

In this paper, a simulated annealing (SA)-based optimisation is carried out for simultaneous estimation of the Reynolds number (Re) and the dimensions of the enclosure (l_x, l_y ) from the knowledge of centreline velocity field. For demonstrating the retrieval methodology, the required centreline velocity field is first obtained from a forward method using some known values of the unknowns, which are ultimately estimated by the inverse method. SA is used to optimise the objective function represented by the square of the difference between the known field and an arbitrary guessed field (calculated using some guessed value of the unknowns). For studying the sensitivity of the estimated parameters, the effect of random errors has been investigated and the suitability of the SA has been checked for different initial guesses. The algorithm reported in the present work is useful in estimating the above unknowns (Re, l_x, l_y ) for a given velocity field.     

A new contribution for the impulsive synchronization of fractional-order discrete-time chaotic systems

In this paper, we discuss and investigate the impulsive synchronization of fractional-order discrete-time chaotic systems. The proposed method is based on the impulsive synchronization theory used in the integer-order case on the one hand and the mathematical analysis of the fractional-order discrete-time systems on the other hand. Sufficient conditions for the stability of synchronization error system are given, and application example with numerical simulations is illustrated in order to verify that the proposed method is applicable and effective. Furthermore, in order to validate the proposed synchronization approach, we have also provided the experimental implementation results using Arduino Mega boards.     

Delay-dependent state estimation for T-S fuzzy delayed Hopfield neural networks

This paper proposes a new delay-dependent state estimator for Takagi–Sugeno (T-S) fuzzy delayed Hopfield neural networks. By employing a suitable Lyapunov–Krasovskii functional, a delay-dependent criterion is established to estimate the neuron states through available output measurements such that the dynamics of the estimation error is asymptotically stable. It is shown that the design of the proposed state estimator for such neural networks can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed state estimator.     

A new dynamic subgrid-scale model using artificial neural network for compressible flow

The subgrid-scale (SGS) kinetic energy has been used to predict the SGS stress in compressible flow and it was resolved through the SGS kinetic energy transport equation in past studies. In this paper, a new SGS eddy-viscosity model is proposed using artificial neural network to obtain the SGS kinetic energy precisely, instead of using the SGS kinetic energy equation. Using the infinite series expansion and reserving the first term of the expanded term, we obtain an approximated SGS kinetic energy, which has a high correlation with the real SGS kinetic energy. Then, the coefficient of the modelled SGS kinetic energy is resolved by the artificial neural network and the modelled SGS kinetic energy is more accurate through this method compared to the SGS kinetic energy obtained from the SGS kinetic energy equation. The coefficients of the SGS stress and SGS heat flux terms are determined by the dynamic procedure. The new model is tested in the compressible turbulent channel flow. From the a posterior tests, we know that the new model can precisely predict the mean velocity, the Reynolds stress, the mean temperature and turbulence intensities, etc.     

A fractional-order model for the novel coronavirus (COVID-19) outbreak

Nonlinear Dynamics - The outbreak of the novel coronavirus (COVID-19), which was firstly reported in China, has affected many countries worldwide. To understand and predict the transmission...     

A new fractional derivative model for linearly viscoelastic materials and parameter identification via genetic algorithms

In this study, a new nested model consisting of springs and “spring pots” is proposed to better simulate the viscoelastic behavior of polymeric damping materials in the frequency domain. First, the one-dimensional constitutive equation that consists of ten parameters is derived. The dynamical mechanical properties, which are the storage modulus, the loss modulus, and the loss factor, are obtained from this equation. Then, the low- and high-frequency behavior of this model is investigated. Moreover, a new methodology to identify the unknown parameters that appear in the fractional derivative model, from the experimental data for the Wicket plot, by using genetic algorithms (GAs) is presented. This approach does not require shifting of the experimental data; therefore, possible errors that may arise are eliminated. The new model is fitted to experimental data for several polymeric damping materials that exist in the literature, in order to verify its success. The results are presented in a graphical form with comparison to the already existing models.     

A network model with free-strand dynamics for polymer melts

 A network model for polymer melts is presented in which disentangled strands relax under flow conditions and may rejoin the network before complete relaxation. For simplicity, we study Gaussian strands that move affinely when incorporated in the network. Network strands are created and lost according to a time constant λ. Free strands have their dynamics given by the Bird-DeAguiar model as a crude representation of reptation and the hindered rotation experienced by polymer strands in melts. The model yields a shear-thinning viscosity with overshoot in the start-up viscosity η⁺ (t). The double-step strain results compare well with available experimental data. Received: 10 July 2000 Accepted: 10 July 2001     

A novel fractional-order model and controller for vibration suppression in flexible smart beam

Nonlinear Dynamics - Vibration suppression represents an important research topic due to the occurrence of this phenomenon in multiple domains of life. In airplane wings, vibration can cause...     

Damage modeling and detection for a tree network using fractional-order calculus

Nonlinear Dynamics - Large networks are increasingly common in engineered systems, and therefore, monitoring their operating conditions is increasingly important. This paper proposes a model-based...     

A stochastic model for parameter identification of adhesive materials

In practice, there are only a very limited number of experimental data available. Therefore, the prediction of material behaviour is difficult and a statistical analysis with a stochastic-based method is nearly impossible. In order to increase the number of tests based on experimental data, we apply the method of stochastic simulation based on time series analysis. The generated artificial data have the same stochastic behaviour as the experimental data. Advantages of artificial data are the arbitrary number of data available, and as a conclusion, the process of parameter identification can be statistically analysed. Here, we especially have experiments for adhesive materials for substantial tension tests performed at two different strain rates. Artificial data provide a stochastic proved analysis of the parameter identification concerning distribution and deviations. The analysis shows the possible range of the different material parameters and, therefore, gives a detailed view of the identification process.     

Analysis and synchronization for a new fractional-order chaotic system with absolute value term

A new fractional-order chaotic system with absolute value term is introduced. Some dynamical behaviors are investigated and analyzed. Furthermore, synchronization of this system is achieved by utilizing the drive-response method and the feedback method. The suitable parameters for achieving synchronization are studied. Both the theoretical analysis and numerical simulations show the effectiveness of the two methods.     

Spline adaptive filter with fractional-order adaptive strategy for nonlinear model identification of magnetostrictive actuator

The spline adaptive filter (SAF) is recently proposed to identify wiener-type nonlinear systems, which consists of an infinite impulse response filter followed by an adaptable look-up table and interpolated by a local low-order polynomial spline curve. To improve the performance of magnetostrictive actuator (MA), SAF is introduced to identify the hysteresis model of MA in this paper. In addition, a direct approach that is convenient to implement to derive the inverse model directly from experimental data is proposed to decrease the difficulty of obtaining the accurate inverse model. In order to improve the identification accuracy, a variable order fractional-order least mean square (VO-FLMS) algorithm is formulated for SAF by exploiting the fractional calculus concepts in parameters adaptation mechanism. VO-FLMS dynamically adapts the order of the fractional derivative based on the error power to achieve faster convergence rate with smaller steady-state error than least mean square algorithm and modified fractional-order least mean square algorithm. Simulation results confirm the effectiveness of SAF with VO-FLMS for nonlinear system identification. In particular, VO-FLMS can adapt nonlinearity better than other compared algorithms. Moreover, the hysteresis model and direct inverse model of MA can be precisely identified online by the proposed method in the experiments.     

Online system identification using fractional-order Hammerstein model with noise cancellation

Slow convergence and low accuracy are two main drawbacks in nonlinear system identification methods. It becomes more complicated when time delay and noises are considered. In this paper, considering a fractional-order Hammerstein model, an online identification method is proposed. A combination of an evolutionary optimization method and recursive least square algorithm is used to estimate the system parameters and orders in the presence of unknown noises. Finally, simulation results are taken to prove the effectiveness of the proposed algorithm.