Lyapunov functions for Lotka–Volterra predator–prey models with optimal foraging behavior

 The theory of optimal foraging predicts abrupt changes in consumer behavior which lead to discontinuities in the functional response. Therefore population dynamical models with optimal foraging behavior can be appropriately described by differential equations with discontinuous right-hand sides. In this paper we analyze the behavior of three different Lotka–Volterra predator–prey systems with optimal foraging behavior. We examine a predator–prey model with alternative food, a two-patch model with mobile predators and resident prey, and a two-patch model with both predators and prey mobile. We show that in the studied examples, optimal foraging behavior changes the neutral stability intrinsic to Lotka–Volterra systems to the existence of a bounded global attractor. The analysis is based on the construction and use of appropriate Lyapunov functions for models described by discontinuous differential equations. Received: 23 March 1999     

Robust stability of genetic regulatory networks with distributed delay

This paper investigates robust stability of genetic regulatory networks with distributed delay. Different from other papers, distributed delay is induced. It says that the concentration of macromolecule depends on an integral of the regulatory function of over a specified range of previous time, which is more realistic. Based on Lyapunov stability theory and linear matrix inequality (LMI), sufficient conditions for genetic regulatory networks to be global asymptotic stability and robust stability are derived in terms of LMI. Two numerical examples are given to illustrate the effectiveness of our theoretical results.     

Global and robust stability of interval Hopfield neural networks with time-varying delays

In this paper, we investigate the problem of global and robust stability of a class of interval Hopfield neural networks that have time-varying delays. Some criteria for the global and robust stability of such networks are derived, by means of constructing suitable Lyapunov functionals for the networks. As a by-product, for the conventional Hopfield neural networks with time-varying delays, we also obtain some new criteria for their global and asymptotic stability.     

Robust exponential stabilization of a class of delayed neural networks with reaction-diffusion terms

In this paper, the problem of global robust exponential stabilization for a class of neural networks with reaction-diffusion terms and time-varying delays which covers the Hopfield neural networks and cellular neural networks is investigated. A feedback control gain matrix is derived to achieve the global robust exponential stabilization of the neural networks by using the Lyapunov stability theory, and the stabilization condition can be verified if a certain Hamiltonian matrix with no eigenvalues on the imaginary axis. This condition can avoid solving an algebraic Riccati equation. Finally, a numerical simulation illustrates the effectiveness of the results.     

On the estimation of robustness and filtering ability of dynamic biochemical networks under process delays, internal parametric perturbations and external disturbances

Inherently, biochemical regulatory networks suffer from process delays, internal parametrical perturbations as well as external disturbances. Robustness is the property to maintain the functions of intracellular biochemical regulatory networks despite these perturbations. In this study, system and signal processing theories are employed for measurement of robust stability and filtering ability of linear and nonlinear time-delay biochemical regulatory networks. First, based on Lyapunov stability theory, the robust stability of biochemical network is measured for the tolerance of additional process delays and additive internal parameter fluctuations. Then the filtering ability of attenuating additive external disturbances is estimated for time-delay biochemical regulatory networks. In order to overcome the difficulty of solving the Hamilton Jacobi inequality (HJI), the global linearization technique is employed to simplify the measurement procedure by a simple linear matrix inequality (LMI) method. Finally, an example is given in silico to illustrate how to measure the robust stability and filtering ability of a nonlinear time-delay perturbative biochemical network. This robust stability and filtering ability measurement for biochemical network has potential application to synthetic biology, gene therapy and drug design.     

Global photosynthetic capacity is optimized to the environment

Earth system models (ESMs) use photosynthetic capacity, indexed by the maximum Rubisco carboxylation rate (V_cmax), to simulate carbon assimilation and typically rely on empirical estimates, including an assumed dependence on leaf nitrogen determined from soil fertility. In contrast, new theory, based on biochemical coordination and co‐optimization of carboxylation and water costs for photosynthesis, suggests that optimal V_cmax can be predicted from climate alone, irrespective of soil fertility. Here, we develop this theory and find it captures 64% of observed variability in a global, field‐measured V_cmax dataset for C₃ plants. Soil fertility indices explained substantially less variation (32%). These results indicate that environmentally regulated biophysical constraints and light availability are the first‐order drivers of global photosynthetic capacity. Through acclimation and adaptation, plants efficiently utilize resources at the leaf level, thus maximizing potential resource use for growth and reproduction. Our theory offers a robust strategy for dynamically predicting photosynthetic capacity in ESMs.     

A sensitive gel-based global O-glycomics approach reveals high levels of mannosyl glycans in the high mass region of the mouse brain proteome

Abstract We developed a gel-based global O-glycomics method applicable for highly complex protein mixtures entrapped in discontinuous gradient gel layers. The protocol is based on in-gel proteolysis with pronase followed by (glyco)peptide elution and off-gel reductive β-elimination. The protocol offers robust performance with sensitivity in the low picomolar range, is compatible with gel-based proteomics, and shows superior performance in global applications in comparison with workflows eliminating glycans in-gel or from electroblotted glycoproteins. By applying this method, we analyzed the O-glycome of human myoblasts and of the mouse brain O-glycoproteome. After semipreparative separation of mouse brain proteins by one-dimensional SDS gel electrophoresis, the O-glycans from proteins in different mass ranges were characterized with a focus on O-mannose-based glycans. The relative proportion of the latter, which generally represent a rare modification, increases to comparatively high levels in the mouse brain proteome in dependence of increasing protein masses.     

变时滞区间细胞神经网络的全局鲁棒稳定性

利用拓扑度理论和Liapunov泛函方法讨论了变时滞区间细胞神经网络的全局鲁棒稳定性．给出了实用有效的判定条件,推广了有关文献中的结果．     

Global robust stability for shunting inhibitory CNNs with delays

In this paper, the problem of global robust stability for shunting inhibitory cellular neural networks (SICNNs) is studied. A sufficient condition guaranteeing the network's global robust stability is established. The result can easily be used to verify globally robust stable networks. An example is given to illustrate that the conditions of our results are feasible.     

Global robust power-rate stability of delayed genetic regulatory networks with noise perturbations

In this paper, by using the Lyapunov method, Itô’s differential formula and linear matrix inequality (LMI) approach, the global robust power-rate stability in mean square is discussed for genetic regulatory networks with unbounded time-varying delay, noise perturbations and parameter uncertainties. Sufficient conditions are given to ensure the robust power-rate stability (in mean square) of the genetic regulatory networks. Meanwhile, the criteria ensuring global power-rate stability in mean square are a byproduct of the criteria guaranteeing global robust power-rate stability in mean square. The obtained conditions are derived in terms of linear matrix inequalities (LMIs) which are easy to be verified via the LMI toolbox. An illustrative example is given to show the effectiveness of the obtained result.     

Finite-time synchronization of coupled neural networks via discontinuous controllers

This paper investigates finite-time synchronization of an array of coupled neural networks via discontinuous controllers. Based on Lyapunov function method and the discontinuous version of finite-time stability theory, some sufficient criteria for finite-time synchronization are obtained. Furthermore, we propose switched control and adaptive tuning parameter strategies in order to reduce the settling time. In addition, pinning control scheme via a single controller is also studied in this paper. With the hypothesis that the coupling network topology contains a directed spanning tree and each of the strongly connected components is detail-balanced, we prove that finite-time synchronization can be achieved via pinning control. Finally, some illustrative examples are given to show the validity of the theoretical results.     

Global stability of population models

Local stability seems to imply global stability for population models. To investigate this claim, we formally define apopulation model. This definition seems to include the one-dimensional discrete models now in use. We derive a necessary and sufficient condition for the global stability of our defined class of models. We derive an easily testable sufficient condition for local stability to imply global stability. We also show that if a discrete model is majorized by one of these stable population models, then the discrete model is globally stable. We demonstrate the utility of these theorems by using them to prove that the regions of local and global stability coincide for six models from the literature. We close by arguing that these theorems give a method for demonstrating global stability that is simpler and easier to apply than the usual method of Liapunov functions.     

带时间延迟的Cohen-Grossberg神经网络全局鲁棒稳定性的一个结果（英文）

在本文中,我们讨论了一类带时间延迟的Cohen-Grossberg神经网络,并研究了这个系统平衡点的全局鲁棒稳定性。利用Lyapunov函数,我们得出了全局鲁棒收敛性的几个充分条件。这些条件以线性矩阵不等式（LMI）的形式表达。因此,从计算的角度出发他们是高效的。另外,这些条件不依赖于时间延迟和神经网络的激发函数。     

On the role of long incubation periods in the dynamics of acquired immunodeficiency syndrome (AIDS)

In this study, we investigate systematically the role played by the reproductive number (the number of secondary infections generated by an infectious individual in a population of susceptibles) on single group populations models of the spread of HIV/AIDS. Our results for a single group model show that if R 1, the disease will die out, and strongly suggest that if R > 1 the disease will persist regardless of initial conditions. Our extensive (but incomplete) mathematical analysis and the numerical simulations of various research groups support the conclusion that the reproductive number R is a global bifurcation parameter. The bifurcation that takes place as R is varied is a transcritical bifurcation; in other words, when R crosses 1 there is a global transfer of stability from the infection-free state to the endemic equilibrium, and vice versa. These results do not depend on the distribution of times spent in the infectious categories (the survivorship functions). Furthermore, by keeping all the key statistics fixed, we can compare two extremes: exponential survivorship versus piecewise constant survivorship (individuals remain infectious for a fixed length of time). By choosing some realistic parameters we can see (at least in these cases) that the reproductive numbers corresponding to these two extreme cases do not differ significantly whenever the two distributions have the same mean. At any rate a formula is provided that allows us to estimate the role played by the survivorship function (and hence the incubation period) in the global dynamics of HIV. These results support the conclusion that single population models of this type are robust and hence are good building blocks for the construction of multiple group models. Our understanding of the dynamics of HIV in the context of mathematical models for multiple groups is critical to our understanding of the dynamics of HIV in a highly heterogeneous population.     

DNA methylation stability in fish spermatozoa upon external constraint: Impact of fish hormonal stimulation and sperm cryopreservation

Highly differentiated mature spermatozoa carry not only genetic but also epigenetic information that is to be transmitted to the embryo. DNA methylation is one epigenetic actor associated with sperm nucleus compaction, gene silencing, and prepatterning of embryonic gene expression. Therefore, the stability of this mark toward reproductive biotechnologies is a major issue in animal production. The present work explored the impact of hormonal induction of spermiation and sperm cryopreservation in two cyprinids, the goldfish (Carassius auratus) and the zebrafish (Danio rerio), using LUminometric Methylation Assay (LUMA). We showed that while goldfish hormonal treatment did increase sperm production, it did not alter global DNA methylation of spermatozoa. Different sperm samples repeatedly collected from the same males for 2 months also showed the same global DNA methylation level. Similarly, global DNA methylation was not affected after cryopreservation of goldfish spermatozoa with methanol, whereas less efficient cryoprotectants (dimethylsulfoxide and 1,2‐propanediol) decreased DNA methylation. In contrast, cryopreservation of zebrafish spermatozoa with methanol induced a slight, but significant, increase in global DNA methylation. In the less compact nuclei, that is, goldfish fin somatic cells, cryopreservation did not change global DNA methylation regardless of the choice of cryoprotectant. To conclude, global DNA methylation is a robust parameter with respect to biotechnologies such as hormonal induction of spermiation and sperm cryopreservation, but it can be altered when the best sperm manipulation conditions are not met.     

Mean square exponential and robust stability of stochastic discrete-time genetic regulatory networks with uncertainties

This paper aims to analyze global robust exponential stability in the mean square sense of stochastic discrete-time genetic regulatory networks with stochastic delays and parameter uncertainties. Comparing to the previous research works, time-varying delays are assumed to be stochastic whose variation ranges and probability distributions of the time-varying delays are explored. Based on the stochastic analysis approach and some analysis techniques, several sufficient criteria for the global robust exponential stability in the mean square sense of the networks are derived. Moreover, two numerical examples are presented to show the effectiveness of the obtained results.     

Finite-time and fixed-time synchronization analysis of inertial memristive neural networks with time-varying delays

This paper investigates the finite-time synchronization and fixed-time synchronization problems of inertial memristive neural networks with time-varying delays. By utilizing the Filippov discontinuous theory and Lyapunov stability theory, several sufficient conditions are derived to ensure finite-time synchronization of inertial memristive neural networks. Then, for the purpose of making the setting time independent of initial condition, we consider the fixed-time synchronization. A novel criterion guaranteeing the fixed-time synchronization of inertial memristive neural networks is derived. Finally, three examples are provided to demonstrate the effectiveness of our main results.     

Existence and global asymptotic stability of positive periodic solutions of n-species delay impulsive Lotka–Volterra type systems

In this paper, the existence and global asymptotic stability of positive periodic solutions of periodic n-species Lotka–Volterra impulsive systems with several deviating arguments are studied. By using the continuation theorem of coincidence degree theory and Lyapunov–Razumikhin method, sufficient conditions are obtained. Some known results are improved and generalized.     

Do young rhesus macaques know what others see?: A comparative developmental perspective

Humans undergo robust ontogenetic shifts in the theory of mind capabilities. Are these developmental changes unique to human development or are they shared with other closely related non-human species? To explore this issue, we tested the development of the theory of mind capacities in a population of 236 infant and juvenile rhesus macaques (Macaca mulatta). Using a looking-time method, we examined what developing monkeys know about others’ perceptions. Specifically, we tested whether younger monkeys predict that a person will reach for an object where she last saw it. Overall, we found a significant interaction between a monkey's age and performance on this task (p = .014). Juvenile monkeys (between two and 5 years of age) show a nonsignificant trend towards human infant-like patterns of performance, looking longer during the unexpected condition as compared to the expected condition, though this difference is nonsignificant (p = .09). However, contrary to findings in human infants, infant rhesus macaques show a different trend. Infant monkeys on average look slightly longer on average during the expected condition than the unexpected condition, though this pattern was not significant (p = .06). Our developmental results in monkeys provide some hints about the development of the theory of mind capacities in non-humans. First, young rhesus macaques appear to show some interest in the perception of other agents. Second, young rhesus seems able to make predictions based on the visual perspective of another agent, though the developmental pattern of this ability is not as clear nor as robust as in humans. As such, though an understanding of others’ perceptions is early-emerging in human infants, it may require more experience interacting with other social agents in our non-human relatives.