Bifurcation and Oscillatory Dynamics of Delayed Cyclic Gene Networks Including Small RNAs

Dynamical Modeling and Qualitative Analysis of a Delayed Model for CD8 T Cells in Response to Viral Antigens

Although the immune effector CD8 T cells play a crucial role in clearance of viruses, the mechanisms underlying the dynamics of how CD8 T cells respond to viral infection remain largely unexplored. Here, we develop a delayed model that incorporates CD8 T cells and infected cells to investigate the functional role of CD8 T cells in persistent virus infection. Bifurcation analysis reveals that the model has four steady states that can finely divide the progressions of viral infection into four states, and endows the model with bistability that has ability to achieve the switch from one state to another. Furthermore, analytical and numerical methods find that the time delay resulting from incubation period of virus can induce a stable low-infection steady state to be oscillatory, coexisting with a stable high-infection steady state in phase space. In particular, a novel mechanism to achieve the switch between two stable steady states, time-delay-based switch, is proposed, where the initial conditions and other parameters of the model remain unchanged. Moreover, our model predicts that, for a certain range of initial antigen load: 1) under a longer incubation period, the lower the initial antigen load, the easier the virus infection will evolve into severe state; while the higher the initial antigen load, the easier it is for the virus infection to be effectively controlled and 2) only when the incubation period is small, the lower the initial antigen load, the easier it is to effectively control the infection progression. Our results are consistent with multiple experimental observations, which may facilitate the understanding of the dynamical and physiological mechanisms of CD8 T cells in response to viral infections.

Large-Scale Neural Networks With Asymmetrical Three-Ring Structure: Stability, Nonlinear Oscillations, and Hopf Bifurcation

A large number of experiments have proved that the ring structure is a common phenomenon in neural networks. Nevertheless, a few works have been devoted to studying the neurodynamics of networks with only one ring. Little is known about the dynamics of neural networks with multiple rings. Consequently, the study of neural networks with multiring structure is of more practical significance. In this article, a class of high-dimensional neural networks with three rings and multiple delays is proposed. Such network has an asymmetric structure, which entails that each ring has a different number of neurons. Simultaneously, three rings share a common node. Selecting the time delay as the bifurcation parameter, the stability switches are ascertained and the sufficient condition of Hopf bifurcation is derived. It is further revealed that both the number of neurons in the ring and the total number of neurons have obvious influences on the stability and bifurcation of the neural network. Ultimately, some numerical simulations are given to illustrate our qualitative results and to underpin the discussion.

Understanding Dynamics and Bifurcation Control Mechanism for a Fractional-Order Delayed Duopoly Game Model in Insurance Market

Recently, the insurance industry in China has been greatly developed. The number of domestic insurance companies and foreign investment insurance companies has greatly increased. Competition between different insurance companies is becoming increasingly fierce. Grasping the internal competition law of different insurance companies is a very meaningful work. In this present work, we set up a novel fractional-order delayed duopoly game model in insurance market and discuss the dynamics including existence and uniqueness, non-negativeness, and boundedness of solution for the established fractional-order delayed duopoly game model in insurance market. By selecting the delay as a bifurcation parameter, we build a new delay-independent condition ensuring the stability and creation of Hopf bifurcation of the built fractional-order delayed duopoly game model. Making use of a suitable definite function, we explore the globally asymptotic stability of the involved fractional-order delayed duopoly game model. By virtue of hybrid controller which includes state feedback and parameter perturbation, we can effectively control the stability and the time of creation of Hopf bifurcation for the involved fractional-order delayed duopoly game model. The research indicates that time delay plays an all-important role in stabilizing the system and controlling the time of onset of Hopf bifurcation of the involved fractional-order delayed duopoly game model. To check the rationality of derived primary conclusions, Matlab simulation plots are explicitly presented. The established results in this manuscript are wholly novel and own immense theoretical guiding significance in managing and operating insurance companies.

An important link between the gut microbiota and the circadian rhythm: imply for treatments of circadian rhythm sleep disorder

Currently, gut microbiota living in the gastrointestinal tract, plays an important role in regulating host's sleep and circadian rhythms. As a tool, gut microbiota has great potential for treating circadian disturbance and circadian insomnia. However, the relationship between gut microbiota and circadian rhythms is still unclear, and the mechanism of action has still been the focus of microbiome research. Therefore, this article summarizes the current evidences associating gut microbiota with factors that impact host circadian rhythms neurology sleep disorder. Moreover, we discuss the changes to these systems in sleep disorder and the potential mechanism of intestinal microbiota in regulating circadian rhythms neurology sleep disorder via microbial metabolites. Meanwhile, based on the role of intestinal flora, it is provided a novel insight into circadian related insomnia and will be benefit the dietary treatment of circadian disturbance and the circadian related insomnia.

Dynamics Analysis and Design for a Bidirectional Super-Ring-Shaped Neural Network With n Neurons and Multiple Delays

Recently, the dynamics of delayed neural networks has always incurred the widespread concern of scholars. However, they are mostly confined to some simplified neural networks, which are only made up of a small amount of neurons. The main cause is that it is difficult to decompose and analyze generally high-dimensional characteristic matrices. In this article, for the first time, we can solve the computing issues of high-dimensional eigenmatrix by employing the formula of Coates flow graph, and the dynamics is considered for a bidirectional neural network with super-ring structure and multiple delays. Under certain circumstances, the characteristic equation of the linearized network can be transformed into the equation with integration element. By analyzing the equation, we find that the self-feedback coefficient and the delays have significant effects on the stability and Hopf bifurcation of the network. Then, we achieve some sufficient conditions of the stability and Hopf bifurcation on the network. Furthermore, the obtained conclusions are applied to design a standardized high-dimensional network with bidirectional ring structure, and the scale of the standardized high-dimensional network can be easily extended or reduced. Afterward, we propose some designing schemes to expand and reduce the dimension of the standardized high-dimensional network. Finally, the results of theories are coincident with that of experiments.

Qualitative Analysis and Bifurcation in a Neuron System With Memristor Characteristics and Time Delay

This article focuses on the hybrid effects of memristor characteristics, time delay, and biochemical parameters on neural networks. First, we propose a novel neuron system with memristor and time delays in which the memristor is characterized by a smooth continuous cubic function. Second, the existence of equilibria of this type of neuron system is examined in the parameter space. Sufficient conditions that ensure the stability of equilibria and occurrence of pitchfork bifurcation are given for the memristor-based neuron system without delay. Third, some novel criteria of the addressed neuron system are constructed for guaranteeing the delay-dependent and delay-independent stability. The specific conditions are provided for Hopf bifurcations, and the properties of Hopf bifurcation are ascertained using the center manifold reduction and the normal form theory. Moreover, there exists a phenomenon of bistability for the delayed memristor-based neuron system having three equilibria. Finally, the effectiveness of the theoretical results is demonstrated by numerical examples.

Bifurcation and oscillatory dynamics of delayed CDK1-APC feedback loop

Extensive experimental evidence has been demonstrated that the dynamics of CDK1-APC feedback loop play crucial roles in regulating cell cycle processes, but the dynamical mechanisms underlying the regulation of this loop are still not completely understood. Here, the authors systematically investigated the stability and bifurcation criteria for a delayed CDK1-APC feedback loop. They showed that the maximum reaction rate of CDK1 inactivation by APC can drive sustained oscillations of CDK1 activity ([inline-formula removed]) and APC activity ([inline-formula removed]), and the amplitude of these oscillations is increasing with the increase of the reaction rate over a wide range; a certain range of the self-activation rate for CDK1 is also significant for generating these oscillations, for too high or too low rates the oscillations cannot be generated. Moreover, they derived the sufficient conditions to determine the stability and Hopf bifurcations, and found that the sum of time delays required for activating CDK1 and APC can induce [inline-formula removed] and [inline-formula removed] to be oscillatory, even when the [inline-formula removed] and [inline-formula removed] settle in a definite stable steady state. Furthermore, they presented an explicit algorithm for the properties of periodic oscillations. Finally, numerical simulations have been presented to justify the validity of theoretical analysis.

Stability and bifurcation analysis of a fractional-order single-gene regulatory model with delays under a novel PDα control law

In this paper, we propose a novel fractional-order proportional-derivative (PD) strategy to achieve the control of bifurcation of a fractional-order gene regulatory model with delays. The stability theory of fractional differential equations proved that with delays, some explicit conditions for the local asymptotical stability and Hopf bifurcation are given for the controlled fractional-order genetic model. It is demonstrated that the fractional-order gene regulatory model becomes controllable by adjusting the control gain parameters. In addition, the effect of fractional-order parameter on the dynamical behaviors is shown. Finally, numerical simulations are carried out to testify the validity of the main results and the availability of the fractional-order PD controller.

Compressive sensing-based topology identification of multilayer networks

Recovering network topologies is of great significance in the study of complex networks. In this paper, a method for identifying structures of multilayer networks is proposed via compressive sensing and Taylor expansion. By using this method, the topologies of multilayer networks with unknown node dynamical functions can be identified from a relatively small number of observations. Numerical experiments are provided to show the effectiveness and efficiency of the method on different types of multilayer networks, where the intralayer topology and the interlayer topology of a multilayer network can be identified simultaneously. In particular, the topology of one layer can be identified even when nodes of the other layer are unobservable.