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One of the most important characteristics of the photovoltaic (PV) modules is their long lifetime (around 25 years). However, recent investigations have shown that PV modules may suffer significant degradation before that time; that is why the development of diagnostic techniques is important for the customers of PV systems. In this paper two indicators to quantify the degradation of a PV module are presented. Such indicators use the single-diode model to represent a PV module without degradation and combine such information with the experimental measurements to estimate the increase in the series resistance and/or the decrease in the parallel resistance with respect to reference values. The estimation of those variations allows the quantification of the module degradation. Simulation results comparing the proposed indicators with the fill factor (a traditional indicator to quantify the electrical quality of a PV module), and other indicators to estimate the series resistance are presented to illustrate the advantages of the proposed indicators. [ABSTRACT FROM AUTHOR]

In this paper, the H ∞ anti-synchronization problem of switching inertial neural networks with constant leakage delays and time-varying mixed delays is addressed. A direct analysis method based on parameterized system solutions is proposed to solve the problem we studied. The advantages of this method are that the variable substitution is not required for the system model and no Lyapunov–Krasovskii functional is constructed, which simplifies the proof process. In addition, the resulting anti-synchronization conditions consisting of some simple scalar inequalities can be easily solved by business softwares, and less computational complexity is involved. It is worth noting that the problem addressed in this paper has not been studied at present, and the limitation on the parity of activation functions in the existing literatures is removed, which reduces conservativeness. Finally, the reliability of the theoretical results is verified by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we construct an improved Implicit–Explicit (IMEX) numerical scheme based on the conservation form of the advection–diffusion equations and study the numerical stability of the method in case of a nonlinear advection–diffusion Lotka–Volterra model. The classical numerical methods might be unsuitable for providing accurate numerical results for advection–diffusion problem in which advection dominates diffusion. An improved numerical scheme is proposed, which can preserve the positivity for arbitrary stepsizes. The convergence, boundedness, existence and uniqueness of the numerical solutions are investigated in paper. A threshold value denoted by R 0 Δ x , is introduced in the stability analysis. It is shown that the numerical semi-trivial equilibrium is locally asymptotically stable if R 0 Δ x < 1 and unstable if R 0 Δ x > 1. Moreover, the limiting behaviors of the threshold value are exhibited. Finally, some numerical simulations are given to confirm the conclusions. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel approach for discretizing the derivative Nonlinear Schrödinger (DNLS) equation in an integrable manner. Our proposed method involves discretizing the time variable, resulting in a discrete system that converges to the DNLS equation in a natural limit. Furthermore, the discrete system retains the same set of infinitely conserved quantities as the original DNLS equation. To demonstrate the effectiveness of our proposed method, we designed a numerical simulation scheme using the Fourier Pseudo-spectral Method to discretize the spatial variable. The numerical results confirm that our new discrete integrable scheme can accurately preserve the conserved quantities of the DNLS equation. [ABSTRACT FROM AUTHOR]

In this paper, considering the spatial propagation behavior of Internet rumor, we propose a new reaction–diffusion rumor propagation model with time delay in social networks. Based on this, we discuss the stability conditions at the equilibrium point and analyze the Turing instability for the approximation propagation system. Simultaneously, the amplitude equations for the approximation system are derived by multiscale analysis. We use numerical simulation to compare the effect of parameter size, period, and time delay on the patterns. Moreover, we compare the different reactivity of the system in the W S networks and the B A networks. Finally, we plot the corresponding amplitude equations patterns by controlling the parameters and verify the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper the three-dimensional extension of the Diffused Vortex Hydrodynamics (DVH) is discussed along with free vorticity dynamics simulations. DVH is a vortex particle method developed in-house and widely validated in a 2D framework. The DVH approach has been embedded in a new frontend to the open-source code PEPC, the Pretty Efficient Parallel Coulomb solver. Within this parallel Barnes–Hut tree code, a superposition of elementary heat equation solutions in a cubic support is performed during the diffusion step. This redistribution avoids excessive clustering or rarefaction of the vortex particles, providing robustness and high accuracy of the method. An ascending vortex dipole at various resolutions is selected as a test-case and heuristic convergence measurements are performed, taking into account the conservation of prime integrals and the energy–enstrophy balance. [ABSTRACT FROM AUTHOR]

In this paper, by taking the NLS-type equations as examples, we propose a novel high-order explicit energy-preserving Lie-group method for Hamiltonian PDEs. The main idea is to combine recently developed generalized SAV (G-SAV) approach (Cheng et al., 2021) and explicit Lie group method, in which the fourth-order or higher-order Lie group method only composes two exponentials in each stage, and this is the key point that the proposed methods can preserve energy of Hamiltonian PDEs. This is our first attempt to construct high-order explicit energy-preserving methods without using projection technique (Hairer et al., 2006 [14]), and some stability conclusions of our proposed methods for the NLS-type equations are also presented. Finally, we present 2D and 3D numerical simulations to demonstrate the stability and accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we provide a framework for the Turing instability in a general two-dimensional discrete reaction–diffusion model that utilizes Euler discretization and coupled map lattices. We obtained explicit criterions for the normal forms of Neimark–Sacker bifurcation and flip bifurcation in the absence of diffusion. We derive the general conditions that govern the emergence of pure Turing instability, Neimark–Sacker–Turing instability, Flip–Turing instability, spatially homogeneous stable states, spatially homogeneous periodic oscillation states, and spatially homogeneous period-doubling oscillatory states under spatially inhomogeneous conditions. As an example, we employ a ratio-dependent predation model and verify the derived general conditions through a series of numerical simulations. Additionally, we apply the calculation of Maximum Lyapunov Exponent(MLE) to simulate and demonstrate the path from flip bifurcation to chaos. [ABSTRACT FROM AUTHOR]

Computer viruses present a substantial threat to our daily lives. Traditional models for the propagation of computer viruses primarily concentrate on network structures. In this paper, we take into account the constrained availability of resources in the context of computer virus prevention and control. We introduce a computer virus propagation model based on resource limitations. By examining the stability of both toxic and non-toxic equilibria within the model, we employ Matlab and Python for numerical analysis to simulate various computer virus propagation scenarios. Additionally, we present corresponding defense mechanisms for combatting these viruses. [ABSTRACT FROM AUTHOR]

We study the implementation of a Chebyshev spectral method with forward Euler integrator proposed in Berardi et al.(2023) to investigate a peridynamic nonlocal formulation of Richards' equation. We prove the convergence of the fully-discretization of the model showing the existence and uniqueness of a solution to the weak formulation of the method by using the compactness properties of the approximated solution and exploiting the stability of the numerical scheme. We further support our results through numerical simulations, using initial conditions with different order of smoothness, showing reliability and robustness of the theoretical findings presented in the paper. • Convergence of a spectral method for a peridynamic formulation of Richards' equation. • Existence and uniqueness of the solution by its stability and compactness properties. • Simulations to numerically verify the existence of the weak solution to the model. [ABSTRACT FROM AUTHOR]

In this paper, a model with spatial diffusion and mixed delays is presented to describe the spread of echinococcosis between dogs and livestock. Firstly, the local stability is investigated using the Routh–Hurwitz criterion. Furthermore, when considering time delays as bifurcation parameters, the conditions for the occurrence of Hopf bifurcation are discussed based on the linear approximation of the nonlinear system. Lastly, the fixed-time stability is studied under the implementation of appropriate control measures. Numerical simulations are provided to give a better understanding of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we study the split common fixed point problem for two nonlinear mappings in p -uniformly convex and uniformly smooth Banach spaces. We propose an algorithm which uses dynamic stepsize, it allows to be easily implemented without prior information about operator norm. We further apply our result to solve the split variational inclusion problem, equilibrium problem and convexly constrained linear inverse problem. Moreover, we provide numerical examples to verify efficiency of our algorithm. • Presents an iteration process for splitting problems, with dynamic choosing step size. • Implement the result for solving wide classes of mathematical engineering problems. • Includes nontrivial example with computer simulation to compare our findings with existing ones. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the classical chemostat model where the consumption function of the species, in both cases Monod and Haldane, is perturbed by real random fluctuations. Once the existence and uniqueness of non-negative global solution of the corresponding random systems is ensured, we prove the existence of a deterministic compact attracting set, whence we are able to find conditions to guarantee either the extinction or the persistence of the species, the most important aim in real applications. In addition, we depict several numerical simulations to illustrate the theoretical framework, standing out our contributions, providing the biological interpretation of every result and comparing with similar works in the literature. [ABSTRACT FROM AUTHOR]

This paper presents the qualitative analysis of a predator–prey model with nonmonotonic functional response and impulsive effects. Different from previous work, by considering two factors of nonmonotonic functional response and impulsive effects, this paper studies the existence and stability of the periodic semi-trivial solution y = 0 first. Then, by constructing an appropriate Poincare map and introducing geometric theory, it is shown that the predator–prey model can exhibit a variety of dynamic phenomena, including orbitally asymptotically stable order-1 periodic solution (O1PS), order-2 periodic solution (O2PS) and globally stable equilibrium point under certain conditions. When there exists an O2PS, its appearance and disappearance as well as the appearance of bifurcation phenomenon are discussed in detail with different selections of the initial value of predator. Finally, numerical simulations illustrate the correctness of the results of the theoretical analysis. The theoretical results presented in this paper can be seen as an advancement to the previous related works. [ABSTRACT FROM AUTHOR]

Chaotic systems are widely used in designing encryption algorithms for their ideal dynamical performances. One-dimensional (1D) chaotic maps have the highest efficiency in implementation and have achieved great attention. However, 1D chaotic maps have a common security weakness, which is that their key space is relatively small. Therefore, in this paper, a cluster of 1D quadratic chaotic maps is proposed according to the topological conjugate theory. The 1D chaotic map has three tunable parameters which have a significant expansion in parameter space than the traditional 1D chaotic maps. The 1D map is proved to be chaotic theoretically since it is topologically conjugated with a logistic chaotic map. An example of a 1D quadratic chaotic map is provided in this paper, and several numerical simulation results indicate that this 1D quadratic map has ideal chaotic characteristics, which are consistent with the theoretical analysis. To verify the effectiveness of this 1D quadratic map, a novel image encryption algorithm is proposed. The security of this image encryption algorithm is completely dependent on the properties of the 1D quadratic map. Security experimental test results show that this image encryption algorithm has a high-security level, and is quite competitive with other chaos-based image encryption algorithms. [ABSTRACT FROM AUTHOR]

Time-delay is a universal phenomenon in control systems, which usually leads to instability and poor performance of systems. In this paper, the p th moment asymptotic stability of trivial solutions to uncertain dynamical systems with time-delays is investigated. The concept of the generalized expected value is introduced with its properties based on uncertainty theory. Sufficient conditions for ensuring the stability of uncertain delay systems are derived by Lyapunov direct method. Several illustrative examples with numerical simulations are arranged to demonstrate the effectiveness of the stability results. [ABSTRACT FROM AUTHOR]

In this paper, a stage-structured predator–prey model is considered in a toxic environment, emphasizing on the affect of the toxic substances on growth of the species in presence of time delays. The positivity and boundedness of solutions have been discussed. The analytical and numerical simulations of the proposed model show that the coexistence equilibrium point is stable for low and moderate values of the delay parameter associated with the predator's maturity. Even though there is an interval of the maturation time in which the system exhibits oscillatory behaviour, a longer maturity duration may lead to the extinction of the predator species. The impact of toxicity on the proposed system is also investigated. The stability of the system repeatedly switches as the time delay, related to the changes of toxicity incurred in the adult predator, varies, and finally becomes unstable for a significant value of it. Besides that, the delay related to the prey's toxicity has also led some exciting results. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a new fractional derivative operator in which the generalized cardinal sine function is used as a non-singular analytic kernel. In addition, we provided the corresponding fractional integral operator. We expressed the new fractional derivative and integral operators as sums in terms of the Riemann–Liouville fractional integral operator. Next, we introduced an efficient extension of the new fractional operator that includes integrable singular kernel to overcome the initialization problem for related differential equations. We also proposed a numerical approach for the numerical simulation of IVPs incorporating the proposed extended fractional derivatives. The proposed fractional operators, the developed relations and the presented numerical method are expected to be employed in the field of fractional calculus. [ABSTRACT FROM AUTHOR]

In this paper, we apply the Z-type control method to a crop-pest–natural enemy model. We consider the indirect Z-controller in the natural enemy population and investigate the mathematical properties of the model. Furthermore, our analytical results are also numerically validated. Our paper supports that the pest population can be controlled by using an indirect Z-control mechanism in the natural enemy population. Investigations on the crop-pest–natural enemy model also highlight how the Z-control method acts in respect to different dynamical regimes of the uncontrolled model. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical and numerical investigation of stationary and oscillatory patterns in a spatial model of bacteria quiescence. The reaction–diffusion model consists of active and inactive microbial populations in a harsh environment accounting for the directed movement and switch of cells to dormancy at high concentration levels. We present a bifurcation analysis of the model and the interplay between Turing and Hopf instability is discussed. Numerical simulations supporting the existence of spatially homogeneous solutions, as well as stable spatial patterns and oscillatory patterns are presented. [ABSTRACT FROM AUTHOR]

Prey-taxis, which plays an important role in biological control and ecological balance, is the phenomenon that predators shift directly toward regions with the highest density of prey. In this paper, we consider a spatiotemporal predator–prey system involving prey-taxis and nonconstant mortality. By structuring Lyapunov functional, we obtain the global stability of spatially homogeneous steady states. The minimal mortality of predator will determine whether they can survive. In addition, we identify the parameter ranges that spatially homogeneous steady state remains stable or becomes unstable, and discuss steady state bifurcation by choosing prey-taxis coefficient. It is found that a diffusion-induced instability can occur under nonconstant mortality, and prey-taxis can annihilate the spatial patterns induced by diffusion. Numerical simulations illustrate that prey-taxis and nonconstant mortality can result in rich pattern formations including spots pattern, spots–strips pattern, labyrinth pattern, strips-like pattern. It is worth noting that the weak prey-taxis is disadvantageous in terms of the number of two species. [ABSTRACT FROM AUTHOR]

This paper explores the role of gradient learning on the convergence of output dynamics in duopoly competition model under incomplete information. For this purpose, we develop two scenarios dynamic co-opetition duopoly models under incomplete information. To this end, the gradient learning is adopted to update the strategy output. We propose dynamic co-opetition duopoly model with homogeneous gradient learning to analyze whether gradient learning enables two firm approach to the Cournot–Nash equilibrium state, when the output dynamics converges to interior stable point meaning the coexistence of two firms. It deduces that gradient learning decreases the profit difference between two firms. Furthermore, we highlight that the dynamics of output converges to the Cournot–Nash equilibrium. We mention dynamic co-opetition duopoly model with heterogeneous gradient learning to explore the survival of the firm that leaves the market, when output dynamics converges to the boundary stable point indicating one firm leaves the market while the other monopolies it. Our conclusion identifies that gradient learning can make the firm that leaves the market enter the market again. Finally, the numerical simulations are presented to verify our results. • Convergence of the strategy is analyzed in dynamic co-opetition duopoly model. • Gradient learning is adopted to update the strategy under incomplete information. • Gradient learning makes the strategy converge to the Cournot–Nash equilibrium. • Gradient learning could change the state whether the disappeared firm survives or not. [ABSTRACT FROM AUTHOR]

In this paper, a modified Leslie-type predator–prey model with simplified Holling type IV functional response is established, in which double Allee effect on prey and nonlinear prey harvesting are considered. The analysis of the model shows that there exists a Bogdanov–Takens singularity (focus case) of codimension 4, and also multiple other nonhyperbolic and degenerate equilibria. Bifurcations are explored and it is found that transcritical bifurcation, saddle–node bifurcation, Bogdanov–Takens bifurcation of codimension 2, degenerate cusp type Bogdanov–Takens bifurcation of codimension 3, and degenerate focus type Bogdanov–Takens bifurcation of codimension 4 occur as parameters vary. The bifurcations result in complex dynamic behaviors, such as double limit cycle, triple limit cycle, quadruple limit cycle, cuspidal loop, (multiple) homoclinic loop, saddle–node loop, and limit cycle(s) simultaneously with homoclinic loop. We run numerical simulations to verify the theoretical results, and it is found that the system admits bistability, tristability, or even tetrastability. [ABSTRACT FROM AUTHOR]

In this paper, we propose a hybrid numerical method based on the weighted finite difference and the quintic Hermite collocation methods. The proposed method is used for solving the variable-order time fractional mobile–immobile advection–dispersion (VOMIM-AD) model, such that the discretization is done by applying collocation method with Hermite splines in the spatial direction and weighted finite difference method in the temporal direction. Provided examples confirm the studied stability and convergence properties of the proposed method. The obtained results from the graphical illustration and numerical simulations, in comparison with other methods in the literature, demonstrate that the reported method is very robust and accurate. [ABSTRACT FROM AUTHOR]

Multiquadric (MQ) quasi-interpolation has been extensively studied in approximation theory and its applications. However, most of them only focus on the case that the sampling data are point-evaluation functionals (discrete function values). This restricts its applications since a more general form of data in real applications is integral functionals (integration of an approximand over subdomains that form a partition of the considering region). In addition, integral functionals also demonstrate characteristics of sampling devices. Therefore it is more meaningful to extend multiquadric quasi-interpolation to integral functionals. The purpose of the paper is to construct such a new multiquadric quasi-interpolation scheme. The scheme possesses the constant reproduction property and thus preserves positivity of an approximand. Moreover, if the approximand is a density function of a random variable, then the resulting quasi-interpolant is also a density function. Thus, as a byproduct, we also provide a scheme for nonparametric kernel density estimation. However, unlike classical kernel density estimation that usually has a boundary bias problem over a bounded domain, our scheme circumvents the problem. Numerical simulations including posteriori error estimates and density estimation are demonstrated at the end of the paper to show efficiency and robustness of the scheme. [ABSTRACT FROM AUTHOR]

This paper discusses numerical solutions for the control functions of parabolic integro-differential equations under the assumption of approximate controllability. It is proved theoretically that the numerical solution for the control function converges to the exact solution, and the validity of the theory is demonstrated from different perspectives through four numerical simulation examples. [ABSTRACT FROM AUTHOR]

Type-1 diabetes mellitus (T1DM) is one of the most extensive diseases in the world. In this disorder, a malfunction occurs in the glucose–insulin regulatory system when one intakes food. Therefore, the synchronization of T1DM and perturbed T1DM models are necessary to transform the disturbance behavior of T1DM into a typical T1DM model. In this paper, a type-1 diabetic mellitus glucose–insulin metabolism (T1DMGIM) model is concerned with a new fractal–fractional operator β ∈ (0 , 1 ] , η ∈ (0 , 1 ] by adding food intake as a disturbance to the plant system. A new generalized differentiation operator is introduced as the convolution of the power law. This new operator is based on the fractal–fractional differentiation and integration operators in the Riemann–Liouville (R-L) sense. Sufficient conditions are achieved for the existence, uniqueness, and stability of an error T1DMGIM model by employing the Mönch contraction principle. Finally, numerical simulations are provided to verify the theoretical results. [ABSTRACT FROM AUTHOR]

This paper concentrates on dynamics and stability analysis of two predators–one prey mathematical model with competition between predators and fading memory in one predator. The investigation of the constructed model shows that there exist five equilibria, e.g. trivial extinction state of all populations, extinction of both predators state, extinction of first or second predator state and coexisting state. Investigating the eigenvalues of characteristic polynomial, conditions for the local stability around each equilibrium are also determined depending on the parameter space. Analytical formulations are complemented with numerical simulations, where time simulations and single parameter numerical continuation of each variable are performed with respect to model parameters and multiple sub-and super-critical Hopf bifurcations, period doubling bifurcation and transcritical bifurcation are detected for different values of memory related parameter. Our results show that fading memory and competition between predators have substantial impact on the existence and dynamics of all three populations and may shed lights on further understanding of interacting species in ecology. • A model comprising one prey and two competitive predators with fading memory is constructed. • Fading memory and competition between predators have a large impact on the dynamics. • Fading memory in one predator may affect the existence and nature of various bifurcations. [ABSTRACT FROM AUTHOR]

In this paper, we study a stochastic predator–prey system with impulsive effects and time periodic coefficients. By the properties of periodic Markov processes, Krylov–Bogolyubov's method and Doob's Theorem, the existence and uniqueness of periodic measure of the system is presented under the condition of the stochastic persistence of the system. Numerical simulations are given to verify the effectiveness of the theoretical results and to show the effects of the stochastic perturbation and impulsive perturbation on the persistence and periodic measure of the system. • We discuss a time-periodic stochastic predator–prey system with impulsive effects. • We obtain the threshold between the persistence and extinction of this system. • We prove that the time-periodic stochastic system has a unique periodic measure. • Numerical simulations have been done to support the analytical results. [ABSTRACT FROM AUTHOR]

The paper proposes control design strategies that minimize the time required by a mobile robot to accomplish a certain task (reach a target) while transmitting/receiving a message. The message delivery is done over a wireless network, and we account for path-loss while disregarding any shadowing phenomena, i.e., the transmission rate depends only on the distance to the wireless antenna. First, using the Pontryagin maximum principle we design a minimal-time control for the simplified robot dynamics described by a single integrator. Next, we show how we can use these theoretical results to efficiently control more complicated non-holonomic dynamics. Numerical simulations illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper deals with regional boundary observability of linear time-fractional systems with Riemann–Liouville derivative. The main purpose is to reconstruct the initial state of the considered system in a subregion B of the boundary ∂ Ω of the evolution domain Ω. For that, we show the link between regional boundary observability on B and regional observability, of the considered system, in a suitable subregion (ω ⊂ Ω) defined such that B ⊂ ∂ ω. This will allow us to firstly recover the initial state in the subregion ω by using an extension of Hilbert Uniqueness Method for fractional systems, after that we take the restriction, on B , of its trace, on ∂ ω , in order to obtain the initial state on B. We also propose an algorithm that enables us to recover the initial state in ω and eventually on B , with a satisfying reconstruction error, which is illustrated in two numerical simulations, using a zonal sensor and a pointwise one. [ABSTRACT FROM AUTHOR]

This paper investigates the numerical approximation of the eigenvalues of regular and singular second-order non-self-adjoint Sturm–Liouville problems using an efficient technique based on the Chebyshev spectral collocation scheme. For this purpose, the spectral differentiation matrices are used to determine the derivatives of Chebyshev polynomials at the grid points and, then convert non-self-adjoint problem into a generalized eigenvalue problem. The convergence associated with this technique has been discussed. Numerical simulations have been conducted to illustrate the excellent performance of this technique and to demonstrate that it is achieving high accuracy and is computationally cost-effective. Numerical results and comparison with other techniques are presented. [ABSTRACT FROM AUTHOR]

The current study presents complex dynamics of an SIR epidemic model that incorporates a saturated type incidence rate as well as treatment. We provide here rigorous results for asymptotic stability of equilibrium states of the proposed system. Several bifurcations including Hopf, Generalized Hopf, saddle–node, transcritical and Bogdanov–Takens are also discussed. The stability of bifurcated periodic solutions is verified with the help of first Lyapunov number. Extensive numerical simulations are performed to validate these results. In a numerical example it is observed that if the saturation factor increases slowly, then the unique endemic equilibrium state is asymptotically stable for a certain range. The further increase in the value of saturation parameter, the endemic equilibrium state loses its stability and periodic solutions appear through Hopf bifurcation. It is also observed that the increase in saturation parameter beyond Hopf bifurcation threshold, results in regaining the stability of the endemic equilibrium state, which forms an interesting dynamical phenomenon in the bifurcation diagram named as an endemic bubble. It is pointed out that in the case of two endemic equilibrium states, one of these two is always saddle, whereas, the other one becomes unstable through Hopf bifurcation. In this scenario, the periodic solution is initially stable and it becomes unstable through generalized Hopf bifurcation. In numerical example for Bogdanov–Takens bifurcation two pairs of feasible bifurcation thresholds exist for the same set of parameters value. The bifurcation diagrams and equilibrium surfaces are also plotted to observe the combined effects of medication and saturation parameters. • In this paper an SIR epidemic model with a saturated type incidence rate as well as treatment is studied. • Stability and bifurcation of all feasible equilibrium states are discussed. • An endemic bubble is observed through Hopf bifurcation in case of unique endemic equilibrium. • Generalized Hopf bifurcation in case of two endemic equilibrium is pointed out. • In case of Bogdanov–Takens bifurcation there are two pairs of feasible bifurcation thresholds. [ABSTRACT FROM AUTHOR]

A characteristic feature of living organisms is their response to the environment in search for food or reproduction opportunities. This paper is devoted to the investigation of the pattern formation of the Holling-Tanner predator–prey model with predator-taxis. We first summarise the qualitative properties of the model where a threshold for the appearance of pattern formation is specified. Then we design and analyse a coupled nonstandard finite difference and finite volume scheme for the proposed model. Numerical simulations are provided to support theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we present a newly proposed local fractional method pertaining to the local fractional Sumudu transform (LFST) for computational study of local fractional Schrödinger's equations (LFSEs). The error analysis for the present method is also discussed here. The uniqueness and convergence analyses for the solution obtained by using the proposed scheme are also established. The numerical simulations for achieved results have been performed for different orders of a local fractional derivative. The results depict that the proposed method efficiently provides the solution for given equations in a smooth manner. [ABSTRACT FROM AUTHOR]

Abstract This paper deals with a Wind Conversion System (WCS) based on a Hybrid Excitation Synchronous Generator (HESG) connected to an isolated load. The set is modeled under Matlab–Simulink. To ensure an efficient and reliable use of the system, a tight control remains vital. In fact, the dynamic equations of a turbine are strongly nonlinear as are the ones of a HESG; most of the system parameters are highly uncertain, and, at last, a WCS is always affected by disturbance sources such as load variances, harmonics, mechanical vibrations...To address these problems, robust control methods must be adopted. In this paper, two strategies for the control of variable speed wind turbine are investigated. First, an H ∞ controller is implemented. Then, a second-generation CRONE controller is designed. The performance of the two regulators is compared with respect to the tracking of the optimal rotation speed, the attenuation of the mechanical vibration and the robustness to the uncertainty of the parameters, using time-domain simulations. It has been found that the CRONE controller is more robust to parameters uncertainty and minimizes the fluctuations of the torsional torque and the generator's angular velocity. Finally, an experimental validation of the velocity controllers is presented to complete the simulation results and fully validate the chosen approach. [ABSTRACT FROM AUTHOR]

Abstract This paper addresses the simulation of complex systems which consider phenomena with different time scales. Such problems are encountered on studies of electrical systems which try to take into account the simulation of the power converter and its control laws, over representative operating cycles of several hours. Moreover, when storage elements are integrated into a power chain, their aging may need the designer to consider larger time scales, which can then exceed a few years. It is the reason why most studies separate the time scales between the slow dynamics for the energetic, thermal and aging phenomena, and the fast ones to study the power converter and its control laws. This paper presents an original cycle-based and multi-rate method for the simulation of power systems with a wide range of time scales and with high mutual dependency between the fast and slow state variables. This method is applied to the supercapacitor energy storage system of a full-electric ferry. The proposed simulation results take into account at the same time the switching of the power converter and the aging of the supercapacitor, with a reduction of the computational effort greater than 1 0 5. In other words, while a full calculation of the problem takes 10 centuries on a personal computer, the proposed method permits to have the same result in only 15 days. Highlights • A simulation framework of multi-time scale modeling. • It relies on cycle-based formulation of the system operation. • Method applied to the energy powertrain of a full-electric ferry. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Emden–Fowler integral equation with Green's function type kernel. We propose three computational algorithms based on the Gegenbauer-wavelet, the Taylor-wavelet, and the Laguerre-wavelet to solve such problems. Firstly, we transform the given problems via the collocations technique to the system of algebraic equations, which are then solved by the Newton–Raphson method to get the required numerical solution. We also provide the error bound of the proposed method. To demonstrate the efficiency of the proposed methods, we consider several examples arising in physical models, including real-life problems. The numerical simulations justify the superiority and high performance of the methods, and the obtained results are compared with some other existing schemes. The comparison shows that the proposed method converges faster than other numerical techniques like Haar-wavelets collocation method, advanced Adomian decomposition method, and simplified reproducing kernel method. The numerical tables and graphs show that the accuracy of the proposed method is very high, even for the few collocation points. The L ∞ and the L 2 errors decrease gradually with an increase in collocation points, and hence, the current method is stable. [ABSTRACT FROM AUTHOR]

In this paper, we explore an ecoepidemic model of a prey–predator type in which the prey population is infected by an SI type disease with two infectious routes (horizontal and vertical). Specifically, we consider that both susceptible and infected preys have emergent carrying capacities, which implies that both preys are involved in intraspecific and interclass competitions. In addition, we assume that the susceptible prey gathers together to defend the predator. It is found that the proposed system exhibits abundant dynamics and admits nine equilibria: three boundary equilibria, three plane equilibria, and three interior equilibria. At least one of the three populations can be eliminated from the ecosystem based on the stability of the previous two types of equilibria. According to the stability of the interior equilibria, the given ecosystem can allow the coexistence of susceptible prey–infected prey–predator. We then investigate the stability and direction of Hopf bifurcation. A sensitivity analysis is also conducted to show the effects of the six parameters which are relevant to the emergent carrying capacity and infectious routes on the studied system. Numerical simulations are conducted to verify our theoretical conclusions. [ABSTRACT FROM AUTHOR]

Active Queue Management (AQM) schemes complement Transmission Control Protocol (TCP) congestion-control mechanisms in reducing queuing delay, packet loss, and in improving network throughput. This paper presents a detailed mathematical review of the control-theoretic AQM feedback structure. We highlight and clarify the misconceptions regarding its usage, and furthermore, we verify and validate the numerical time-domain and event-domain simulations of existing AQM schemes using the MATLAB-Simulink platform and the NS-3 simulator platform respectively. Finally, conclusions and some future research directions are briefly discussed. [ABSTRACT FROM AUTHOR]

Numerically asymmetric force field is examined in particle-oriented problems such as Quasicontinuum modeling and simulation. To configure the ground state of a large-scale physical system featured by numerically asymmetric force field, we propose a Hessian-free Newton–Raphson method where the Newton equation is solved using central-difference based BiCGstab algorithm (denoted as HFNR-BiCGstab-diff for simplicity). A detailed analytical and experimental investigation on the convergence performance of the HFNR-BiCGstab-diff algorithm is given in this paper. A pure HFNR-BiCGstab-diff algorithm may suffer from unreliable start-up, particularly in the case that the initial guess is far from the minimizer. As a remedy, a hybrid method that couples HFNR-BiCGstab-diff with preconditioned nonlinear conjugate gradient algorithm (PNCG) is developed to achieve optimal computational performance. The algorithms addressed in this paper have been implemented using POSIX-Thread C++. Their performance has been evaluated using three-dimensional Quasicontinuum simulation problems, which are featured by asymmetric force field and large dimensional sizes up to 122,808 degree-of-freedom, as benchmarks. The numerical experiment on IBM SP2 demonstrates that, compared to alternative unconstrained optimization methods such as preconditioned nonlinear conjugate gradient algorithm, the hybrid algorithm saves 20%–60% running time. [ABSTRACT FROM AUTHOR]

This paper describes the mathematical modeling of a parabolic trough collector where the heat transfer fluid has temperature dependent physical properties for which we have developed our own mathematical expressions. For a specific location and date, the direct solar radiation and other sun–earth parameters are computed on a Julian day basis. Also, we have used certain known and recent correlations for the heat transfer coefficients appearing in this model. The mathematical model is governed by three nonlinear partial differential equations of parabolic type with initial/boundary value conditions. We describe a numerical algorithm in order to obtain the approximate solution of this model. Then, we carry out some numerical simulations which yield valuable information for the performance and efficiency of a solar PTC plant at the specific location. [ABSTRACT FROM AUTHOR]

In this paper, we propose a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. The key idea, in contrast to the standard two-point gradient method, is to use multiple search directions in each iteration without extra computation, and to get the step size by metric projection. Moreover, a modified discrete backtracking search algorithm is proposed to select the combination parameters in the accelerated two-point gradient method. Under the basic assumptions for iterative regularization methods, we establish the convergence results of the method in the noise-free case. Furthermore, stability and regularity are presented when the algorithm terminated by the discrepancy principle for the case of noisy data. Finally, some numerical simulations are presented, which exhibit that the proposed method leads to a significant reduction of the iteration numbers and the overall computational time. [ABSTRACT FROM AUTHOR]

With both analytical and numerical methods, chaotic motions of the Rayleigh–Duffing oscillator with a non-smooth periodic perturbation and harmonic excitation are investigated in this paper. Chaos arising from homoclinic or heteroclinic intersections is studied with the Melnikov method. Chaos threshold is obtained and chaotic feature on the system parameters is investigated in detail. Some new interesting dynamic phenomena including "controllable frequency interval", "chaotic band" and "uncontrollable parameters" are presented and proved rigorously. Numerical simulations are given to verify chaos threshold obtained by the analytical results. [ABSTRACT FROM AUTHOR]

In this paper we discuss the dynamical properties of stochastic Hepatitis C model that describes its transmission. At the beginning, the existence and uniqueness of global positive solution of system are proven. As for the stability properties, first the stability in probability of disease-free equilibrium is obtained. Then, we establish the conditions under which extinction of the disease from the population occurs. Also, the conditions for the parameters of the model under which the solution of the system is persistent in mean are found. In the end, we use numerical simulations to confirm our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a Gause type predator–prey system with constant-yield prey harvesting and monotone ascending functional response is proposed and investigated. We focus on the influence of the harvesting rate on the predator–prey system. First, equilibria corresponding to different situations are investigated, as well as the stability analysis. Then bifurcations are explored at nonhyperbolic equilibria, and we give the conditions for the occurrence of two saddle–node bifurcations by analyzing the emergence, coincidence and annihilation of equilibria. We calculate the Lyapunov number and focal values to determine the stability and the quantity of limit cycles generated by supercritical, subcritical and degenerate Hopf bifurcations. Furthermore, the system is unfolded to explore the repelling and attracting Bogdanov–Takens bifurcations by perturbing two bifurcation parameters near the cusp. It is shown that there exists one limit cycle, or one homoclinic loop, or two limit cycles for different parameter values. Therefore, the system is susceptible to both the constant-yield prey harvesting and initial values of the species. Finally, we run numerical simulations to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper presents the study of fractional Emden–Fowler (FEF) equations by utilizinga new adequate procedure, specifically the q- homotopy analysis transform method (q- HATM). The EF equation has got greater significance in both physical and mathematical investigation of capillary and nonlinear dispersive gravity waves. The projected technique is tested by considering four illustrations of the time-fractional EF equations. The q -HATM furnish ℏ , known as an auxiliary parameter, by the support of ℏ we can modulate the various stages of convergence of the series solution. Additionally, to certify the resolution and accurateness of the proposed method we fitted the suitable numerical simulations. The redeem results guarantee that the proposed process is more convincing and scrutinizes the extremely nonlinear issues emerging in the field of science and engineering. • q -HATM is applied to obtain the solution to fractional Emden-Fowler equations. • Accuracy of the proposed method is validated through suitable numerical simulations. • The proposed method is efficient to study nonlinear issues in the areas of science. [ABSTRACT FROM AUTHOR]

In the paper, to better understand the dynamic relationship between Microcystis aeruginosa and filter-feeding fish, we have constructed a new aquatic ecological model to describe the aggregation effect of Microcystis aeruginosa. Mathematical theory works mainly investigated the critical threshold condition through the discovery of transcritical bifurcation, saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation. The numerical simulation works mainly revealed that Microcystis aeruginosa aggregation effect has played an important role in the dynamic relationship with the aid of bifurcation analysis, which also in turn proved the validity of theoretical derivation. The results showed that if the Microcystis aeruginosa aggregation area became larger and larger, and exceeded a critical threshold, the filter-feeding fish would eventually go extinct. Furthermore, it should be stressed that Microcystis aeruginosa aggregation can effectively control the feeding dynamic behavior of filter-feeding fish and provide shelter from predators. Finally, all these results were expected to be useful in studying population dynamics of some aquatic ecosystems. [ABSTRACT FROM AUTHOR]

Every outbreak of a serious infectious disease has the potential to pose unprecedented challenges to humanity. Understanding how epidemic spreads among populations is a key step in preventing and controlling it to spread. In this paper, for modeling the epidemic spreading and its associated information spreading, we put forward a novel coupled two-layered networking framework. One layer deals with the modeling of an SI 1 I 2 R process, where each node in the network may be in four states: susceptible, mildly infected, severely infected and recovery. Whereas, for the other layer, the transmission dynamics can be represented by an unaware–aware–refractory (UAT) model, which is significantly different from the classical unaware–aware–unaware (UAU) process since there exist individuals who are unwilling to share information. Moreover, we set a group of discrete time Microscopic Markov equations and derive the epidemic threshold. Finally, some numerical simulations are carried out to validate the analytical results. This work is of great significance to prevent epidemic, and it can be applicable in guiding the input on disease-related information on complex networks. [ABSTRACT FROM AUTHOR]

In this paper, we study finite-time (FET) and fixed-time (FDT) bipartite synchronization of complex networks (CNs) with signed graphs. Under the framework of signed graphs, the interactions between nodes can be either collaborative or antagonistic, which are different from the traditional CNs. Two types of control schemes without the sign function are designed to realize FET and FDT bipartite synchronization of CNs, respectively. By 1-norm analytical techniques and Lyapunov functional method, FET bipartite synchronization criterion is established. By means of the constructed comparison system, FDT bipartite synchronization is proved. In addition, the settling times of both FET synchronization and FDT synchronization are estimated. It is worth noting that the settling time of FDT bipartite synchronization is not related to the initial values. Moreover, numerical simulations are given to illustrate the new results. [ABSTRACT FROM AUTHOR]