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Specific activator and repressor transcription factors which bind to specific regulator DNA sequences, play an important role in gene activity control. Interactions between genes coding such transcripion factors should explain the different stable or sometimes oscillatory gene activities characteristic for different tissues. In this paper, the dynamic P53-Mdm2 interaction model with distributed delays is investigated. Both weak and Dirac kernels are taken into consideration. For Dirac case, the Hopf bifurcation is investigated. Some numerical examples are finally given for justifying the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper is studied a chemical phenomenon, an example of an autocatalytic reaction. Using the stability in first approximation and the theory of bifurcations is studied the stability the autocatalytic reaction. The mathematical modelling was made using the Maple software. [ABSTRACT FROM AUTHOR]

A key focus of this paper is on understanding stability in a non-linear circuit design subject to delayed feedback. [ABSTRACT FROM PUBLISHER]

DC distribution is becoming more and more a suitable technical solution for medium voltage (MV) distribution systems especially in presence of storage devices and renewable energy sources. Among the different challenging issues concerning the new topological configurations of DC systems, stability represents a topic of paramount importance. The paper presents, by means of numerical continuation method, the stability analysis of two DC distribution systems which supply constant power loads (CPLs) connected to the AC grid with an interface converter. CPLs behavior may provoke voltage instability of the DC systems. The paper presents the approach used to maximize, by means of a feedback action on the interface converter, the stable region of operation of the DC distribution systems. [ABSTRACT FROM PUBLISHER]

In this paper, a partial dependent prey-predator model with discrete and distributed delays is studied by using the theory of functional differential equation and Hassard's method, the conditions on which positive equilibrium exists and Hopf bifurcation occurs are given, finally, numerical simulations are also included. [ABSTRACT FROM PUBLISHER]

In this paper, a delayed predator-prey model incorporating a constant prey refuge and diffusion is studied. By analyzing the characteristic equation of linearized system corresponding to the model, we study the local asymptotic stability of the postive equilibrium of the system. Hopf bifurcation is occured. By using the normal form and the center manifold theory, an explicit algorithm to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived. Finally, numerical simulations are performed to support the analytical results. With delay increasing, chaotic behaviors are observed. [ABSTRACT FROM PUBLISHER]

In this paper, the Genesio system with distributed time delay feedback is studied. Its linear stability is investigated based on the Routh-Hurwitz criteria. After the local asymptotic stability is analyzed, Hopf bifurcation is demonstrated by choosing the mean time delay as a bifurcation parameter. The direction and the stability criteria of the bifurcating periodic solutions are determined by applying the normal form theory and the center manifold theorem. Fianlly, some numerical simulations are presented to verify the effectiveness of the theoretical results. [ABSTRACT FROM PUBLISHER]

In this paper we consider a model with time delay, which describe tumor growth depending on vascular mass and regulation of new vessel formation through a key angiogenic factor. This model presents a Hopf bifurcation. Also, the stochastic approach is taken into consideration. [ABSTRACT FROM AUTHOR]

Automotive brake squeal is a disruptive high frequency sound radiation phenomenon generated by friction-induced self-excited vibrations of the brake system. The brake system loses its stability and starts oscillating in a limit cycle with amplitudes limited by nonlinearities, the main origin of the nonlinearities being brake lining material. In order to perform a reliable brake squeal prediction using established mathematical-mechanical models, the knowledge of the lining material properties is of great importance. The present paper deals with the experimental identification of lining material properties, expecially referring to the elastic properties. Since these strongly vary depending on the operating conditions of brake systems, it is necessary to reproduce the operating conditions during brake squeal as close as possible in experimental setups. In this context a special test rig, the test data evaluation and the experimentally determined nonlinear elastic brake lining properties are presented. Assuming these brake lining properties to be the prominent source of the nonlinearity, a nonlinear stability analysis is performed on a realistic disk brake model. The results referring to brake squeal are discussed, whereas basic phenomena known from operating experience of brake systems can be explained on the basis of this analysis. [ABSTRACT FROM AUTHOR]

For a single-machine infinite-bus system with thyristor controlled series capacitor(TCSC), a new approach is proposed to solve Hopf bifurcation point of dynamic voltage stability by reduced order, and the feature of the proposed approach is to reduce the order of a (3n+2)-dimensional Newton iterative equations to a (n+2)-dimensional linear equations. Comparing with traditional direct calculation method, the calculation burden can be mitigated and avoided curse of dimensionality, so it is suitable to the analysis and calculation of dynamic voltage stability of a single-machine infinite-bus system. By the nonlinear analysis software package-Auto97, the dynamic voltage stability of a single-machine infinite-bus system is studied in detail with the method proposed in this paper. The test in this example shows that the bifurcation theory can be more accurate than the linearization method in analyzing the dynamical stability near the critical point of the power systems. [ABSTRACT FROM PUBLISHER]

The paper deals with the stability and Hopf bifurcation of a class of a neuron model with reaction-diffusion and delay-dependent parameter. Based on stability and bifurcation theory, determining the delay as the bifurcation parameter, we give some criteria for stability and Hopf bifurcation. Numerical simulations are given to validate the theoretical analysis. It shows that controllers which are designed in this paper can control the occurrence of bifurcation effectively and can dominate the amplitude of the bifurcation limit cycle. [ABSTRACT FROM PUBLISHER]

Experimental evidence points increasingly to the importance of miRNA on circadian rhythms. MiRNA can regulate some key clock genes' expression by stimulating degradation of mRNA and/or repression of translation. In this paper, miRNA is incorporated into a simple model of Drosophila circadian clock with dimerization and proteolysis of PER and TIM. We analytically derive the theoretical results of globally asymptotic stability and provide the conditions for oscillation of the system. Furthermore, the influences of miRNA on the amplitude and period of oscillation are examined by simulation. It is shown that distinct period profiles as a function of miRNA production rate occur. [ABSTRACT FROM PUBLISHER]

In this paper, a neural network system with the different delay-couplings has been established. The effects of the time delays on system dynamics are investigated. The multiple delays greatly complicate the analysis of stability and Hopf bifurcation. By analyzing the corresponding characteristic equation of the trivial equilibrium point, the delay-independent instability criteria are derived, i.e. under which the system will remain the instability for arbitrary delays. Then the conditions of delay-dependent asymptotic stability are investigated in detail. The periodical behaviors can be found when time delays are fixed in the unstable regions. Furthermore, we find that the system exhibits the multiple switches of the stability and instability. At last, some numerical simulations are included to illustrate our theory results. [ABSTRACT FROM PUBLISHER]

In this article we deal with the Hutchinson's equation with distributed delay dx(t)/dt= rx(t)(1-a1x(t)-a2(t-τ)-a3∫t8734f(t-s)x(s)ds where r,τ, a1,a2,a3 are positive constants and f is the delay kernel function. By analyzing the associated characteristic equation, the local stability of positive equilibrium and Hopf bifurcation are investigated. The bifurcation here is controlled by the time delay. Some numerical simulations are performed to verify and illustrate the analytical findings. [ABSTRACT FROM AUTHOR]

This paper studies a delayed singular prey-predator economic model, which is described by differential-algebraic equations due to a economic theory. Local stability and Hopf bifurcation condition are described on the delayed singular prey-predator economic model. It reveals the sensitivity of the model dynamics on gestation time delay. A phenomenon of Hopf bifurcation occurs as the gestation time delay increases through a certain threshold. Numerical simulations are carried out to substantiate these theory analysis. [ABSTRACT FROM PUBLISHER]

When we research the stability and bifurcation of one dimensional delay differential equation, the problem that is met firstly is the estimation for the roots of the characteristic equation including transcendental functions. At present, there have been many methods that can solve the above problem. But the common character of these methods is that can give the partition of the characteristic roots only in the coefficient space or delay space. In this paper, we are devoted to discuss the characteristic equation of one dimensional delay differential equation, by using τ-D decomposition. We provide a Hopf bifurcation diagram of the zero solution of the one dimensional delay differentia equation in the parameter space that is made up of the coefficient and the delay, one can determine the stability domain of the equilibrium and Hopf bifurcation curves in this parameter space according to the partition of the roots of the characteristic equation. [ABSTRACT FROM PUBLISHER]

In this paper, a class of neutral neural networks with delays is considered. The explicit formulas for determining the direction of Hopf bifurcation and stability of bifurcating periodic solutions are derived. Some numerical simulations are carried out to support the analytic results. [ABSTRACT FROM PUBLISHER]

This paper presents an analysis with nonlinear tools for stability in systems dominated by the interconnection of power electronics and supplied by distributed generation. Systems like renewable and not renewable energy sources can supply power to the micro-grid, and their loads can behave as CPL. Hence, the search of Hopf bifurcation points is used to prevent oscillations and instabilities in the system. [ABSTRACT FROM PUBLISHER]

Power system voltage security assessment is generally applied by considering the steady-state stability surface. However, as seen in the literature, random perturbations can drive the system away from stable operation, long before the steady-state stability surface is reached. [ABSTRACT FROM PUBLISHER]

A three stage-structured prey-predator model with hunting delay is studied. The characteristic equations of the boundary and positive equilibrium are analyzed and the conditions of the positive equilibrium occurring Hopf bifurcation are given by applying the theorem of Hopf bifurcation. By using Nyquist criterion, the estimation of the length of delay to preserve stability is obtained. Finally, numerical simulation and brief conclusion are given. [ABSTRACT FROM PUBLISHER]

The nonlinear Lorenz equations govern many physical problems, namely the chaotic behavior in some physical systems. The linearization approach of these equations near stationary points is investigated and some aspects of the chaotic behavior are discussed. [ABSTRACT FROM AUTHOR]

Two advertising systems were linearly coupled via the first variable, with time delay. The stability and the Hopf bifurcation corresponding to the symmetric equilibrium point (the origin) in the 4D system are analyzed. Different types of oscillations corresponding to the limit cycles are compared. [ABSTRACT FROM AUTHOR]