Narrow Results

This paper deals with a new type of synchronization scheme for chaotic neural networks with delays, called modified function projective synchronization, in which chaotic neural networks synchronize up to a scaling function matrix. Based on the nonlinear state observer, a control scheme is derived through the placement technique by designing a state-observer of the derived system to synchronize chaotic neural networks up to a scaling function matrix. This technique, capable of adjusting the scaling function factor arbitrarily for the value of scaling function factor, has no effect on the controllability of error system. That overcomes some limitation in earlier literature. A chaotic cellular neural network and a chaotic Hopfield neural model are used as numerical examples to demonstrate the effectiveness of the proposed synchronization technique.

In this paper, to deal with the problem of modified function projective synchronization (MFPS) between two different networks with delayed couplings and delayed nodes of different dimensions, a hybrid control scheme combining adaptive control and nonlinear control is proposed. First, a more realistic drive-response complex network model is constructed by introducing double delays. Then, we design hybrid feedback controllers to synchronize up the drive and response networks of different dimensions to a scaling function matrix. Based on Lyapunov stability theory and the linear matrix inequality (LMI), we rigorously prove that the MFPS between the proposed drive-response networks can be achieved and meanwhile some sufficient conditions are derived by adopting an appropriate Lyapunov–Krasovskii energy function. Noteably, many existing synchronization settings can be regarded as special cases of the present synchronization framework. Numerical simulation experiments are employed to verify the correctness and the effectiveness of the proposed method.

In this paper, a mathematical model describing the transmission dynamics of onchocerciasis with distributed delays in infection incubation and recovery in humans and blackfly host population is formulated. We showed that the delayed model is positively invariant and bounded. Also, we obtain the onchocerciasis-free and endemic steady-state solutions as well as the basic reproduction number $R_{hb}$ of the delayed onchocerciasis model. We found that the delayed onchocerciasis model is locally asymptotically stable whenever $R_{hb}<1$. The findings suggest that, for $R_{hb}$ to be less than unity, effective use of ivermectin drug for treatment, distribution of treated nets and cloths, etc., is necessary for the minimization and possible elimination of onchocerciasis infection.

In recent years, neutral-type differential-difference equations have been applied extensively in the field of engineering, and their dynamical behaviors are more complex than that of the delay differential-difference equations. In this paper, the equations used to describe a neutral-type neural network system of differential difference equation with two delays are studied (i.e. neutral-type differential equations). Firstly, by selecting ${\tau }_1$, ${\tau }_2$ respectively as a parameter, we provide an analysis about the local stability of the zero equilibrium point of the equations, and sufficient conditions of asymptotic stability for the system are derived. Secondly, by using the theory of normal form and applying the theorem of center manifold introduced by Hassard et al., the Hopf bifurcation is found and some formulas for deciding the stability of periodic solutions and the direction of Hopf bifurcation are given. Moreover, by applying the theorem of global Hopf bifurcation, the existence of global periodic solution of the system is studied. Finally, an example is given, and some computer numerical simulations are taken to demonstrate and certify the correctness of the presented results.

The stability of stochastic recurrent neural networks with time-varying delays is investigated. A set of novel sufficient conditions on almost sure exponential stability has been established. Two examples are also given to illustrate the effectiveness of our results.

In this paper, the dynamical behaviors of a single Hindmarsh–Rose neuron model with multiple time delays are investigated. By linearizing the system at equilibria and analyzing the associated characteristic equation, the conditions for local stability and the existence of local Hopf bifurcation are obtained. To discuss the properties of Hopf bifurcation, we derive explicit formulas to determine the direction of Hopf bifurcation and the stability of bifurcated periodic solutions occurring through Hopf bifurcation. The qualitative analyses have demonstrated that the values of multiple time delays can affect the stability of equilibrium and play an important role in determining the properties of Hopf bifurcation. Some numerical simulations are given for confirming the qualitative results. Numerical simulations on the effect of delays show that the delays have different scales when the two delay values are not equal. The physiological basis is most likely that Hindmarsh–Rose neuron model has two different time scales. Finally, the bifurcation diagrams of inter-spike intervals of the single Hindmarsh–Rose neuron model are presented. These bifurcation diagrams show the existence of complex bifurcation structures and further indicate that the multiple time delays are very important parameters in determining the dynamical behaviors of the single neuron. Therefore, these results in this paper could be helpful for further understanding the role of multiple time delays in the information transmission and processing of a single neuron.

In this paper, we investigate the dynamics of a five-dimensional virus model incorporating saturation incidence rate, CTL immune response and three time delays which represent the latent period, virus production period and immune response delay, respectively. We begin this model by proving the positivity and boundedness of the solutions. Our model admits three possible equilibrium solutions, namely the infection-free equilibrium $E_0$, the infectious equilibrium without immune response $E_1$ and the infectious equilibrium with immune response $E_2$. Moreover, by analyzing corresponding characteristic equations, the local stability of each of the feasible equilibria and the existence of Hopf bifurcation at the equilibrium point $E_2$ are established, respectively. Further, by using fluctuation lemma and suitable Lyapunov functionals, it is shown that $E_0$ is globally asymptotically stable when the basic reproductive numbers for viral infection $R_0$ is less than unity. When the basic reproductive numbers for immune response $R_1$ is less than unity and $R_0$ is greater than unity, the equilibrium point $E_1$ is globally asymptotically stable. Finally, some numerical simulations are carried out for illustrating the theoretical results.

In this paper, the impacts of multiple time delays on a gene regulatory network mediated by small noncoding RNA is studied. By analyzing the associated characteristic equation of the corresponding linearized system, the asymptotic stability of the positive equilibrium is investigated and Hopf bifurcation is demonstrated. Furthermore, the explicit formulae for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are given by the center manifold theorem and the normal form theory for functional differential equations. Finally, some numerical simulations are demonstrated for supporting the theoretical results.

This study develops a general model of delayed p53 regulatory network in the DNA damage response by introducing microRNA 192-mediated positive feedback loop based on the existing research work. Through theoretical analysis and numerical simulation, we find that the delay as a bifurcation parameter can drive the p53-Mdm2 module to undergo a supercritical Hopf bifurcation, thereby producing oscillation behavior. Moreover, we demonstrate how the positive feedback loop formed by p53* and microRNA 192 (miR-192) with the feature of double-negative regulation produces oscillations. Further, a comparison is given to demonstrate that microRNA 192-mediated positive feedback loop affects the robustness of system oscillations. In addition, we show that ataxia telangiectasia mutated kinase (ATM), once activated by DNA damage, makes p53* undergo two Hopf bifurcations. These results reveal that both time delay and miR-192 play tumor suppressing roles by promoting p53 oscillation or high level expression, which will provide a perspective for promoting the development of anti-cancer drugs by targeting miR-192 and time delay.

In this paper, a phytoplankton and zooplankton relationship system with two delays is investigated whose coefficients are related to one of the two delays. Firstly, the dynamic behaviors of the system with one delay are given and the stability of positive equilibrium and the existence of periodic solutions are obtained. Using the fact that the system may occur, the stable switching phenomenon is verified. Under certain conditions, the periodic solutions will exist in a wide range as the delay gets away from critical values. Fixing the delay $\tau$ in the stable interval, it is revealed that the effect of ${\tau }_1$ can also cause the vibration of system. This explains that two delays play an important role in the oscillation behavior of the system. Furthermore, using the crossing curve methods, the stable changes of the positive equilibrium in two-delays plane are given, which generalizes the results of systems for which the coefficients do not depend on delay. Some numerical simulations are provided to verify the theoretical results.

The dynamic behavior of a new financial system with diffusion effect and two delays is studied. The local stability of equilibrium is studied by analyzing the corresponding characteristic equation and developing the crossing curve method. Hopf bifurcation curves are obtained by three procedures and the critical value of delay of Hopf bifurcation is obtained. By using the central manifold theorem and the normal form theory of partial differential equations, the normal form of Hopf bifurcation with two delays is derived, and the bifurcation direction and the stability of periodic solution are determined. The numerical simulations not only verify these theoretical results, but also show that double Hopf bifurcation may occur and the two delays play a key role in chaos suppression. This study has important theoretical value of innovation and practical value in the macro-economic system.

A closed-loop drug delivery system is constructed in which external negative feedback is used to regulate the dynamics of a time-delayed negative feedback mechanism which regulates hormone concentration. This results in a control system composed of two time-delayed negative feedback loops arranged in parallel. Stability regions in parameter space and the location of steady states are determined for the cases when the time delays are equal and when they are unequal. The advantage of this paradigm for drug delivery is that both the steady states and stability of the multiple loop feedback system can be influenced in a precisely controllable manner.

We apply the noncompactness measure by Mawhin to establish sufficient conditions for the existence and uniqueness (EU) of solution to a nonlinear Cauchy problem. The aforesaid problem is investigated under impulsive and nonlinear integral boundary conditions. Further, the problem under consideration contains Caputo-type fractional-order derivative while two different kinds of delay are also involved. After establishing the existence results, we derive some adequate results for the stability analysis of Hyers–Ulam (HU) type. Here, it should be kept in mind that the proposed tools can reduce the strong compact condition by weaker compactness. For justification, we provide some examples also.

We consider an infinite horizon bargaining game in which a deadline can arise with positive probability and where players possess an endogenous commitment device. We show that for any truncation of the game, the equilibrium agreement can only take place if the deadline arises within this finite horizon. Since the deadline is an uncertain event, the equilibrium exhibits agreements which are delayed with positive probability.

In groundwater construction projects, many variables affect construction schedule and cost overruns. This paper aims to examine and evaluate the relative importance of the main factors that cause delay and cost overruns in groundwater construction projects. In order to identify these factors, a questionnaire survey was conducted. Questionnaires were sent to professionals involved in groundwater construction projects in Ghana. The data was analyzed and ranked, based on the profession of the respondents and their roles in the industry (i.e. owners, contractors and consultants). The questionnaire survey consisted of 49 factors which were grouped into nine major categories, and the level of importance of the categories was measured and ranked by the relative importance weights. The percentage agreements in ranking among the three groups were measured. The results shows that: (1) the surveyed groups generally agreed that the project financing category is the main reason for groundwater construction delay and cost overruns, whereas the labor category is the least; (2) owners, consultants and contractors substantially agree on the ranking of the major categories of delay and cost overruns factors. The paper concludes that all the three groups felt that project financing, micro-economics, natural conditions and materials factor categories play a predominant role in causing delay and cost overruns to groundwater construction projects.

Slime mould Physarum polycephalum propagates on nutrient substrates similarly to auto-waves in nonlinear media. In experimental laboratory studies we uncover that the width of geometrically constrained substrate affects the speed of Physarum propagation. We show that Physarum slows down when the width of the substrate increases. The slime mould propagates quicker from the vertex of a triangle to its base than from the base to the vertex. Physarum grows quicker in narrow channels than in wider channels. One can also slow down Physarum propagation by making a finite size expansion of the otherwise narrow channel. In computational experiments with a binary state cellular automaton model we demonstrate that a limitation on the slime mould's body mass production rate could be an underlying mechanism for the width-dependent slowdown of Physarum propagation.

In this paper, we concern a class of the generalized delayed stochastic predator–prey models with feedback controls based on discrete observations. The existence of global positive solution is given first. Then we discuss the deterministic model briefly, and establish the necessary conditions and the sufficient conditions for almost-sure extinction and persistence in mean for the stochastic system, where we show that the feedback controls can change the properties of the population systems significantly. Finally, numerical simulations are introduced to support the main results.

In this paper, we consider a Cohen–Grossberg neural network with three delays. Regarding time delays as a parameter, we investigate the effect of time delays on its dynamics. We show that there exist stability switches for time delays under certain conditions and the conditions for the existence of periodic oscillations are given by discussing the associated characteristic equation. Numerical simulations are given to illustrate the obtained results and interesting network behaviors are observed, such as multiple stability switches of the network equilibrium and synchronous (asynchronous) oscillations.

In this paper, a delayed mathematical model was developed based on experimental data to understand how the time delays required for transcription and translation in Mdm2 gene expression affect the kinetic behavior of the p53-Mdm2 network. Taking the time delays as the main research parameters, the stability of the system at the positive equilibrium was studied by using the theoretical method of delay differential equation. We found that such delays can induce oscillations by undergoing a supercritical Hopf bifurcation. Then, we used the normal form theory and the center manifold reduction to study the direction and stability of the bifurcation in detail. Furthermore, we also studied the effects of the length of time delays and the model parameters by numerical simulations. We found that time delays in Mdm2 synthesis are required for p53 oscillations and the length of such delays can determine the amplitude and period of the oscillations. In addition, the model parameters can also change the stability of the system. These results illustrate that the repair process after DNA damage can be regulated by varying time delays and the model parameters.

In this paper, we study the Hopf bifurcation of predator–prey system with two delays and disease transmission. Furthermore, the global existence of bifurcated periodic solution was studied, the influence of disease transmission is given. At last, some simulations are given to support our result.