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In the recent paper entitled “Hopf bifurcation analysis and ultimate bound estimation of a new 4-D quadratic autonomous hyper-chaotic system” in [Appl. Math. Comput. 291 (2016) 323–339] by Amin Zarei and Saeed Tavakoli, they proposed the following new four-dimensional (4-D) quadratic autonomous hyper-chaotic system: x 1 ˙ = a ( x 2 − x 1 ) , x 2 ˙ = b x 1 − x 2 + e x 4 − x 1 x 3 , x 3 ˙ = − c x 3 + x 1 x 2 + x 1 2 , x 4 ˙ = − d x 2 , which generates double-wing chaotic and hyper-chaotic attractors with only one equilibrium point. Combining theoretical analysis and numerical simulations, they investigated some dynamical properties of that system like Lyapunov exponent spectrum, bifurcation diagram, phase portrait, Hopf bifurcation, etc. In particular, they formulated a conclusion that the system has the ellipsoidal ultimate bound by employing the method presented in the paper entitled “Ultimate bound estimation of a class of high dimensional quadratic autonomous dynamical systems” [Int. J. Bifurc. Chaos, 21(09) (2011), 2679–2694] by P. Wang et al. However, by means of detailed theoretical analysis, we show that both the conclusion itself and the derivation of its proof in [Appl. Math. Comput. 291 (2016) 323–339] are erroneous. Furthermore, we point out that the method adopted for studying the ultimate bound of that system is not applicable at all. Therefore, the ultimate bound estimation of that system needs further studying in future work. [ABSTRACT FROM AUTHOR]

• Existence of T-periodic solution for a stochastic Crowley-Martin model with impulse is investigated. • Asymptotical stability in probability for the Crowley-Martin model is discussed. • Existence and ergodicity of stationary distribution for the Markov switching case are studied. • Our conclusion improves and generalizes the corresponding existing ones. This paper systematically investigates a stochastic Crowley-Martin predator-prey model. Firstly, we derive sufficient conditions for the existence of positive T -periodic solution for the impulsive case. Secondly, distinguished from the previous papers, asymptotical stability in probability is investigated by combining Khasminskii theory of stability with Lyapunov method. Our conclusion also improves and extends the corresponding existing ones. Thirdly, we establish the sufficient criteria for the existence of a unique ergodic stationary distribution for the Markovian switching case. Finally, two numerical examples are presented to demonstrate the effectiveness and feasibility of our analytical results and reveal the respective effect of white noises and Markovian switching. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we pay attention to the problem of particle evacuation from a high-pressure region. This research was inspired by the known problem of the explosion suppression by a cloud of inert and solid particles. This issue has been so far investigated experimentally where the most important tasks have been to find the proper suppressant, estimate its quantity, as well as design the quenching device. Also some attention has been paid to numerical investigation where by use of computer simulation the same questions have been asked. In this paper, we focus on the numerical study, where the first moment of the suppressing process is analysed: the exact behaviour of the particle cloud as it interacts with the gas. A mathematical model is presented that bases on the Eulerian–Lagrangian approach for the description of the gas and solid phases. Finally, some results are shown: both snapshots of particle location as well as some statistics, such as particle cloud area and particle distribution within the cloud. According to the observations, we obtain different behaviour especially if the particle diameter varies. For some values the particles do not seem to be well-distributed and an example are smaller particles that tend to gather along the edges of the eddies formed in the gas phase. [Copyright &y& Elsevier]

In this paper, the stability problem of impulsive functional differential equations (IFDEs) is considered. Several criteria ensuring the uniform stability of IFDEs with finite or infinite delay are derived by establishing some new Razumikhin conditions. Different with the current existing ones, our development results can be applied to delay systems with persistent impulsive effects. Finally, an example and its computer simulation is given to show the effectiveness and advantages of the proposed method. [ABSTRACT FROM AUTHOR]

This paper deals with a parabolic equation with variable coefficient modeling MEMS technology, and we will prove the solution of the problem quenches in finite time in the case without stationary solutions. Numerical simulations are presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper analyses the numerical convergence and the approximation of the finite element method applied to a biothermal nonlinear model for the bare foot. As far as we know, there is not a previous finite element analysis of this well-known bioheat equation. Thus, this work can be seen as a first step to study the coupling with energy and mass transfer models (water, vapor and gas) at the textiles surrounding the foot. The model is posed as a steady partial differential equation for the temperature field, and a non-linear boundary condition on the external boundary, where heat losses due to convection, radiation and evaporation are considered. The existence and the uniqueness of the solution is proved for the weak formulation and also for its finite element approximation by using arguments of monotone operators. Then, numerical convergence and an a priori error estimates result are obtained. Some numerical simulations are presented to show the accuracy of the numerical method and the behavior of the solution, being qualitatively acceptable and, in some cases, validated against experimentation, being quantitatively correct too. Interesting conclusions are followed from the analysis of the model parameters as well as from the comparison of 2D and 3D solutions. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of discontinuous periodic solutions for a class of Liénard systems with state impulses, whose solutions are interrupted by abrupt changes of state. By employing Poincaré mapping method, a criterion for the existence of at least one discontinuous periodic solution in the impulsive Liénard systems is established. Finally, we give an example to illustrate the effectiveness of our result, and the corresponding numerical simulation is presented to show that there is a good agreement between our theoretical result with the computer numerical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the disease dynamics of a reaction–diffusion Feline Panleukopenia virus model incorporating direct and indirect transmissions as well as spatially environmental heterogeneity. We derive a basic reproduction number and show that the disease-free equilibrium will be locally stable if the basic reproduction number is below one, which means that the disease will be extinct. Furthermore, we perform some numerical simulations to explore the impact of the heterogeneous environment on the disease dynamics. [ABSTRACT FROM AUTHOR]

Abstract: Various kinds of finite elements are proposed and employed for one-dimensional wave-field simulations, each of which has their own capabilities and disadvantages. This paper deals with structural similarities and differences that arise at the element level, by the use of reduced forms of mass and stiffness matrices. General parameterized forms are then developed for mass and stiffness matrices of n-noded elements (elements with n nodes with arbitrary arrangement). Optimization for the free parameters will deliver elements with better performance and less numerical dispersion error. Two of such elements are developed and compared for their ability in dispersion-error remission. [Copyright &y& Elsevier]

Abstract: This paper is concerned with a stage-structured predator–prey system with Crowley–Martin functional response. By analyzing the characteristic equation, the local stability of the equilibria is investigated. The persistence of system and global asymptotic stability of the positive equilibrium are carried out. Finally, several numerical simulations to illustrate the theoretical analysis are also given. [Copyright &y& Elsevier]

Abstract: This paper presents a robust numerical method for the analysis of wave propagation in nematic liquid crystals. The structure is excited by a plane wave incident at an oblique angle with respect to the normal to the liquid–crystal cell. The underlined formulation is based on an eigenvalue problem which is solved analytically in order to obtain the governing field expressions inside a homogeneous, thin crystal layer. The liquid–crystal cell is comprised of N such layers. Enforcing the continuity of the tangential electric and magnetic fields at the interfaces formed by the various layers, a matrix system is generated. Solution of the linear system of equations results in the light intensity inside the liquid crystal, which is coupled to a non-linear differential equation for the director tilt angle. This equation is solved using either an explicit or implicit finite-difference scheme. An iteration process continues until convergence is reached for the coupled problem. The proposed numerical method was validated against published results that were generated by approximate analytical methods. Further simulations and studies were conducted emphasizing on the physics of the problem and related interesting phenomena. [Copyright &y& Elsevier]

Abstract: In this paper, the problem of natural convection in a circular eccentric annulus filled with micropolar fluid has been numerically investigated using Fourier Spectral Method. The annulus inner wall is heated and maintained at constant temperature while the outer wall is cooled and kept at constant temperature. The full governing equations of momentum, angular momentum and energy have been solved to give the details of flow and thermal fields. The heat convection process in the annulus is mainly controlled by Rayleigh number Ra, Prandtl number Pr, radius ratio Rr, eccentricity, e and material parameters of micropolar fluid. The material parameters are dimensionless spin gradient viscosity λ, dimensionless micro-inertia density B and dimensionless vortex viscosity D. This study considers Ra up to 5×104 and the eccentricity is varied between −0.6 and +0.6 while dimensionless material parameters D of micropolar fluid is considered between 0 and 10. Both Pr, and Rr are fixed at 0.7, 2.6, respectively while B and λ are assigned the value of 1. The study considers the effect of controlling parameters on flow and thermal fields with emphasis on the effect of these parameters on mean Nusselt number. The study has shown that for certain controlling parameters the heat transfer in the annulus is minimum at a certain eccentricity. The study also has shown that as parameter D increases the rate of heat transfer through the annulus decreases. [Copyright &y& Elsevier]

Abstract: In this paper, we construct a ecological system with prey-taxis. From the dynamic point of view we analytically and numerically investigate the steady states. Our results show how the combined action of the death rates, chemotaxis, diffusivity and conversion efficiency to influence the survival ability of multiple consumer levels in a ecological system with self-produced nutriment. Furthermore, the food chain length of our model can be determined by the co-existence conditions of all consumer levels. Numerical simulation corroborates the analytical results. [Copyright &y& Elsevier]

Abstract: In this paper, a new complex-valued recurrent neural network (CVRNN) called complex-valued Zhang neural network (CVZNN) is proposed and simulated to solve the complex-valued time-varying matrix-inversion problems. Such a CVZNN model is designed based on a matrix-valued error function in the complex domain, and utilizes the complex-valued first-order time-derivative information of the complex-valued time-varying matrix for online inversion. Superior to the conventional complex-valued gradient-based neural network (CVGNN) and its related methods, the state matrix of the resultant CVZNN model can globally exponentially converge to the theoretical inverse of the complex-valued time-varying matrix in an error-free manner. Moreover, by exploiting the design parameter , superior convergence can be achieved for the CVZNN model to solve such complex-valued time-varying matrix inversion problems, as compared with the situation without design parameter involved (i.e., the situation with ). Computer-simulation results substantiate the theoretical analysis and further demonstrate the efficacy of such a CVZNN model for online complex-valued time-varying matrix inversion. [Copyright &y& Elsevier]

Abstract: In this paper, a competitive Lotka–Volterra system with three delays is investigated. By choosing the sum of three delays as a bifurcation parameter, we show that in the above system, Hopf bifurcation at the positive equilibrium can occur as crosses some critical values. And we obtain the formulae determining direction of Hopf bifurcation and stability of the bifurcating periodic solutions by using the normal form theory and center manifold theorem. Finally, numerical simulations supporting our theoretical results are also included. [Copyright &y& Elsevier]

Abstract: In this paper, we give an additive result for the Drazin inverse with its applications, we obtain representations for the Drazin inverse of a 2×2 complex block matrix having generalized Schur complement equal to zero or nonsingular. Several situations are analyzed and recent results are generalized [R.E. Hartwig, X. Li, Y. Wei, Representations for the Drazin inverse of a block matrix, SIAM J. Matrix Anal. Appl. 27 (3) (2006) 757–771]. [Copyright &y& Elsevier]

Abstract: In this paper we obtain the sharp lower bound for , for functions f that are k-uniformly convex in the unit disk U. Next we consider the problem of finding the minimum of for functions f that are k-uniformly convex in the disk of radius r. Corresponding results for the class of starlike functions related to the class of k-uniformly convex functions are presented. [Copyright &y& Elsevier]

Abstract: In this paper, using three distinct computational methods we obtain some new exact solutions for the generalized modified Degasperis–Procesi equation (mDP equation) We show the graph of some of the new solutions obtained here with the aim to illustrate their physical relevance. Mathematica is used. Finally some conclusions are given. [Copyright &y& Elsevier]

In this paper, a novel high dimensional spatiotemporal chaotic system based on 2D non-adjacent coupled map lattice (2DNACML) model is proposed. Each local lattice is influenced by other random lattices in different dimensions and the local map is defined as a fractional-like style. From the theoretical analysis and numerical simulation, it is found that ranges of system parameters are expanded and unfixed in the novel 2DNACML model. As a result, the changed system is improved and been applied in the image encryption with a mixed scrambling scheme with chaotic method and knights tour method and an efficient diffusion scheme for different images to show the effectiveness of the proposed system. [ABSTRACT FROM AUTHOR]