Periodic and nonperiodic oscillatory behavior in a model for activated sludge reactors

A dynamic model for an activated sludge process is proposed to investigate the stability and bifurcation characteristics of this industrially important unit. The model is structured upon two processes: an intermediate participate product formation and active biomass synthesis processes. The growth kinetics expressions are based on substrate inhibition and noncompetitive inhibition of the intermediate product. The bifurcation analysis of the process model shows static as well as periodic behavior over a wide range of model parameters. The model also exhibits other interesting stability characteristics, including bistability and transition from periodic to nonperiodic behavior through period doubling and torus bifurcations. For some range of the reactor residence time the model exhibits chaotic behavior as well. Practical criteria are also derived for the effects of feed conditions and purge fraction on the dynamic characteristics of the bioreactor model.     

Stability analysis of the continuous ethanol fermentation process with a delayed product inhibition

In the paper, we propose and analyze a mathematical model of the continuous ethanol fermentation process to study the mechanisms of the self-sustained oscillations of ethanol concentration. The model is based on the assumption that microorganism cells response to the inhibitory effect of product (ethanol) concentration with a delay. From the local stability analysis of the system, we show that the delay time is one of the crucial factors for the occurrence of oscillations and for a critical delay time the fermentation process undergoes a Hopf bifurcation. Further analysis shows that the operating variables and kinetic parameters have also a significant effect on the dynamical behavior of the fermentation system. A proper manipulation of the operating variables allow us to eliminate the oscillatory behavior.     

Optimal product design using a colony of virtual ants

The optimal product design problem, where the “best” mix of product features are formulated into an ideal offering, is formulated using ant colony optimization (ACO). Here, algorithms based on the behavior of social insects are applied to a consumer decision model designed to guide new product decisions and to allow planning and evaluation of product offering scenarios.     

一类具有Allee影响的捕食者-食饵扩散系统研究

讨论一类具有Allee影响的捕食者-食饵扩散模型解的整体性态.通过线性化方法和Lyapunov泛函方法分别证明了该模型正平衡点的局部渐近稳定性和全局渐近稳定性.     

Existence and Approximation of Solutions of a System of Quasilinear Differential Equations

This paper deals with the behavior, approximation and stability of some solutions of the system of quasilinear differential equations. The behavior of solutions in the neighbourhood of an arbitrary curve is considered, with extraordinary attention on some special cases. The obtained results contain an answer to the question on approximation as well as stability of solutions whose existence is established. The errors of the approximation are defined by the function that can be sufficiently small. The theory of qualitative analysis of differential equations and topological retraction method are used.     

Chaotic Dynamics of a Delayed Discrete-Time Hopfield Network of Two Nonidentical Neurons with no Self-Connections

A bifurcation analysis is undertaken for a discrete-time Hopfield neural network of two neurons with two delays, two internal decays and no self-connections, choosing the product of the interconnection coefficients as the characteristic parameter for the system. The stability domain of the null solution is found, the values of the characteristic parameter for which bifurcations occur at the origin are identified, and the existence of Fold/Cusp, Neimark–Sacker and Flip bifurcations is proved. All these bifurcations are analyzed by applying the center manifold theorem and the normal form theory. It is shown that the dynamics in a neighborhood of the null solution become more and more complex as the characteristic parameter grows in magnitude and passes through the bifurcation values. Under certain conditions, it is proved that if the magnitudes of the interconnection coefficients are large enough, the neural network exhibits Marotto’s chaotic behavior.      

A Five-Dimensional System of Navier-Stokes Equation for a Two-Dimensional Incompressible Fluid on a Torus

A five-mode truncation of Navier-Stokes equation for a two-dimensional incompressible fluid on a torus is studied. Its stationary solutions and stability are presented, the existence of attractor and the global stability of the system are discussed. The whole process, which shows a chaos behavior approached through an involved sequence of bifurcations with the changing of Reynolds number, is simulated numerically. Based on numerical simulation results of bifurcation diagram, Lyapunov exponent spectrum, Poincare section, power spectrum and return map of the system are revealed.     

Navier-Stokes方程五模类Lorenz方程组的动力学行为及数值仿真

本文对平面正方形区域上不可压缩的Navier-Stokes方程,进行傅立叶展开后,截断得到五模类Lorenz方程组.给出了该方程组定常解及其稳定性的讨论,证明了该方程组吸引子的存在性,并对其全局稳定性进行了分析和讨论,数值模拟了雷诺数在一定范围内变化时,类Lorenz方程组的动力学行为.     

一类非线性生化系统的定性分析

研究了一类非线性生化系统的定性行为，给出了该系统极限环的不存在性、存在性、惟一性和稳定性的充分条件，补充和完善了戴林勋(1999)的结论。     

Global character of a host-parasite model

In this paper, we study the qualitative behavior of a discrete-time host-parasite model. Moreover, the periodicity nature of positive solutions, local asymptotic stability, global behavior of unique positive equilibrium point, and its rate of convergence is discussed. Some numerical examples are given to verify our theoretical results.     

Analysis of a viral infection model with delayed immune response

It is well known that the immune response plays an important role in eliminating or controlling the disease after human body is infected by virus. In this paper, we investigate the dynamical behavior of a viral infection model with retarded immune response. The effect of time delay on stability of the equilibria of the system has been studied and sufficient condition for local asymptotic stability of the infected equilibrium and global asymptotic stability of the infection-free equilibrium and the immune-exhausted equilibrium are given. By numerical simulating,we observe that the stationary solution becomes unstable at some critical immune response time, while the delay time and birth rate of susceptible host cells increase, and we also discover the occurrence of stable periodic solutions and chaotic dynamical behavior. The results can be used to explain the complexity of the immune state of patients.     

Dynamic strategic interaction between an innovating and a non-innovating incumbent

This paper analyzes the effects of product innovation on the firms’ investment behavior in a dynamic duopoly framework. A differential game setting is considered where initially two firms are active on a homogeneous product market. One of the firms has an option to introduce a new product that is horizontally and vertically differentiated from the established product. The resulting differential game has three states corresponding to three capital stocks: one for each firm to produce the established product, and one for the innovating firm to produce the new product. We numerically derive Markov perfect equilibria. One of the most remarkable results is that in most cases the non-innovating firm benefits when the other firm carries out the innovation option. The intuition is that, to increase demand for the innovative product, the innovative firm reduces capacity on the established market, which increases the price of the established product and thus the payoff of the non-innovating firm.     

Dynamics of a Delay Logistic Equation with Slowly Varying Coefficients

Computational Mathematics and Mathematical Physics - The existence, stability, and asymptotic behavior of steady modes for a delay logistic equation with slowly varying coefficients are analyzed.     

Stability of the linear complementarity problem at a solution point

In this paper we study the behavior of a solution of the linear complementarity problem when data are perturbed. We give characterizations of strong stability of the linear complementarity problem at a solution. In the case of stability we give sufficient and necessary conditions.     

Dynamic behavior and chaos control in a complex Riccati-type map

This paper is devoted to analyze the dynamic behavior of a Riccatitype map with complex variables and complex parameters. Fixed points and their asymptotic stability are studied. Lyapunov exponent is computed to indicate chaos. Bifurcation and chaos are discussed. Chaotic behavior of the map has been controlled by OGY feedback control method.     

Stability and Hopf bifurcation analysis in a TCP fluid model

In this paper the Hopf bifurcation behavior of a TCP fluid model of Internet congestion control system is investigated. The parameter condition that the Hopf bifurcation occurs is deduced. The stability and direction of the bifurcating periodic solutions are analyzed by applying the normal form theory and the center manifold theorem. Numerical simulations demonstrate the complex behavior of the system and verify the theoretical analysis.     

Qualitative analysis of a reaction–diffusion system

In this paper, we study the qualitative analysis of a reaction–diffusion system. The local stability of the trivial steady state, as well as the blow-up behavior of the solution are obtained.     

社会化媒体环境下不可辩解型产品伤害危机演化博弈研究

社会化媒体的普及改变了信息传播模式,使得产品伤害危机的演化发生了变化。针对社会化媒体环境下不可辩解型产品伤害危机构建演化博弈模型,并引入前景理论构建收益矩阵,对社会化媒体环境下不可辩解型产品伤害危机的演化稳定策略进行分析,通过数值仿真发现社会化媒体环境下不可辩解型产品伤害危机演化中存在:损失规避态度的变化对企业-消费者利益损失的影响存在非对称性现象;合理的政府协调补偿会引导企业和消费者进行策略调整,从而有利于危机的快速平息;外界干预对企业-消费者责任性的影响存在非对称性现象,舆论等干预会对企业行为起到责任约束作用。     

Differential systems, the mapping over period for which is represented by a product of three exponential matrixes

For some periodic differential systems the sufficient conditions of a representation of the mapping over period as a product of a three exponential matrix of the special aspect are obtained. Obtained results are used for research of problems of the existence and stability of periodic solutions of nonlinear systems and the asymptotic orbital stability of cycles of autonomous differential systems.     

Existence and asymptotic behavior of solutions for a mathematical ecology model with herd behavior

In this work, we consider a prey-predator model with herd behavior under Neumann boundary conditions. For the system without diffusion, we establish a sufficient condition to guarantee the local asymptotic stability of all nontrivial equilibria and prove the existence of limit cycle of our proposed model. For the system with diffusion, we consider the long time behavior of the model including global attractor and local stability, and the Hopf and steady-state bifurcation analysis from the unique homogeneous positive steady state are carried out in detail. Furthermore, some numerical simulations to illustrate the theoretical analysis are performed to expand our theoretical results.