Global Stability of a System of Two Interacting Species with Convective and Dispersive Migration

Using Liapunov's direct method, effects of convective and dispersive migration on the global stability of the equilibrium state of a system of two interacting species are investigated. It is shown that the stable equilibrium state without dispersal remains so with dispersal. Further, it is pointed out that stability or instability of the equilibrium state of the system is not affected by convective migration. These results are justified in cases of a system of mutualistic interactions of species and a prey-predator system with functional response.     

延迟遗传调控网络稳定性及分支

本文主要研究了延迟遗传调控网络的局部稳定性和该网络的Hopf分支存在条件．延迟遗传调控网络是无穷维系统,此类系统在平衡点线性化后的特征方程为超越方程。通过对此超越方程进行研究,得到了系统系数不同时的系统稳定的条件及相关结论,又进一步说明了此系统的Hopf分支存在条件．最后,举一个例子进行了数值仿真验证了所得到的结论．     

Stability analysis of a continuum-based constrained mixture model for vascular growth and remodeling

A stabilizing criterion is derived for equations governing vascular growth and remodeling. We start from the integral state equations of the continuum-based constrained mixture theory of vascular growth and remodeling and obtain a system of time-delayed differential equations describing vascular growth. By employing an exponential form of the constituent survival function, the delayed differential equations can be reduced to a nonlinear ODE system. We demonstrate the degeneracy of the linearized system about the homeostatic state, which is a fundamental cause of the neutral stability observations reported in prior studies. Due to this degeneracy, stability conclusions for the original nonlinear system cannot be directly inferred. To resolve this problem, a sub-system is constructed by recognizing a linear relation between two states. Subsequently, Lyapunov’s indirect method is used to connect stability properties between the linearized system and the original nonlinear system, to rigorously establish the neutral stability properties of the original system. In particular, this analysis leads to a stability criterion for vascular expansion in terms of growth and remodeling kinetic parameters, geometric quantities and material properties. Numerical simulations were conducted to evaluate the theoretical stability criterion under broader conditions, as well as study the influence of key parameters and physical factors on growth properties. The theoretical results are also compared with prior numerical and experimental findings in the literature.     

Mathematical analysis of Mayer waves

The goal of this paper is to explore the low-frequency oscillations of arterial pressure in humans, also called Mayer waves. We carefully describe the cardiovascular control system in order to analyse how its different components may be involved in the occurrence of sustained oscillations. We carry out an analysis of stability leading to the definition of a stability index, which we use to study the influence of each control parameter on the stability of the cardiovascular system. We show that all major components of the control system are probably implicated in the appearance of Mayer waves, substantiating recent clinical results in human as well as experimental findings in rats.     

Optimal Placement of Unified Power Flow Controllers to Improve Dynamic Voltage Stability Using Power System Variable Based Voltage Stability Indices

This study examines a new approach to selecting the locations of unified power flow controllers (UPFCs) in power system networks based on a dynamic analysis of voltage stability. Power system voltage stability indices (VSIs) including the line stability index (LQP), the voltage collapse proximity indicator (VCPI), and the line stability index (L_mn) are employed to identify the most suitable locations in the system for UPFCs. In this study, the locations of the UPFCs are identified by dynamically varying the loads across all of the load buses to represent actual power system conditions. Simulations were conducted in a power system computer-aided design (PSCAD) software using the IEEE 14-bus and 39- bus benchmark power system models. The simulation results demonstrate the effectiveness of the proposed method. When the UPFCs are placed in the locations obtained with the new approach, the voltage stability improves. A comparison of the steady-state VSIs resulting from the UPFCs placed in the locations obtained with the new approach and with particle swarm optimization (PSO) and differential evolution (DE), which are static methods, is presented. In all cases, the UPFC locations given by the proposed approach result in better voltage stability than those obtained with the other approaches.     

Stability analysis for a peri-implant osseointegration model

We investigate stability of the solution of a set of partial differential equations, which is used to model a peri-implant osseointegration process. For certain parameter values, the solution has a ‘wave-like’ profile, which appears in the distribution of osteogenic cells, osteoblasts, growth factor and bone matrix. This ‘wave-like’ profile contradicts experimental observations. In our study we investigate the conditions, under which such profile appears in the solution. Those conditions are determined in terms of model parameters, by means of linear stability analysis, carried out at one of the constant solutions of the simplified system. The stability analysis was carried out for the reduced system of PDE’s, of which we prove, that it is equivalent to the original system of equations, with respect to the stability properties of constant solutions. The conclusions, derived from the linear stability analysis, are extended for the case of large perturbations. If the constant solution is unstable, then the solution of the system never converges to this constant solution. The analytical results are validated with finite element simulations. The simulations show, that stability of the constant solution could determine the behavior of the solution of the whole system, if certain initial conditions are considered.     

The geometrical analysis of a predator-prey model with two state impulses

Using successor functions and Poincaré-Bendixson theorem of impulsive differential equations, the existence of periodical solutions to a predator-prey model with two state impulses is investigated. By stability theorem of periodic solution to impulsive differential equations, the stability conditions of periodic solutions to the system are given. Some simulations are exerted to prove the results.     

湖滨湿地生态系统稳定性评价

根据生态系统稳定性的产生原因,将稳定性划分为系统整体稳定性和系统结构稳定性。从系统的稳定性出发,以生态系统的整体稳定性和结构稳定性两个方面为对象,对湖滨湿地生态恢复所产生的生态效益进行了研究。针对系统整体稳定性,给出了生物多样性指数、自然保护区比重和自然灾害等级3个评价指标,并介绍了相应的指标量化方法。与此同时结合能值理论,准确地分析了湖滨湿地生态系统的结构稳定性,为评价湖滨湿地生态恢复的生态效益评价提供了客观的标尺。     

Combined harvesting of a stage structured prey–predator model incorporating cannibalism in competitive environment

In this paper, we propose a prey–predator system with stage structure for predator. The proposed system incorporates cannibalism for predator populations in a competitive environment. The combined fishing effort is considered as control used to harvest the populations. The steady states of the system are determined and the dynamical behavior of the system is discussed. Local stability of the system is analyzed and sufficient conditions are derived for the global stability of the system at the positive equilibrium point. The existence of the Hopf bifurcation phenomenon is examined at the positive equilibrium point of the proposed system. We consider harvesting effort as a control parameter and subsequently, characterize the optimal control parameter in order to formulate the optimal control problem under the dynamic framework towards optimal utilization of the resource. Moreover, the optimal system is solved numerically to investigate the sustainability of the ecosystem using an iterative method with a Runge–Kutta fourth-order scheme. Simulation results show that the optimal control scheme can achieve sustainable ecosystem. Results are analyzed with the help of graphical illustrations.     

A mathematical model of the stability control of human thorax and pelvis movements during walking

A mathematical model is developed to study the human thorax and pelvis movements in the frontal plane during normal walking. The model comprises of two-link base-excited inverted pendulums with one-degree of rotational freedom for each link. Since the linear motion of the pelvis has a significant effect on the upper body stability, this effect is included in the model by having a base point moving in the frontal plane in a general way. Furthermore, because the postural stability is the primary requirement of normal human walking, the control law is developed based on Lyapunov's stability theory, which guarantees the stability of the pendulum system around the up-right position. To evaluate the model, the simulation results, including the angular displacement of each link and the torque applied on each link, are compared with those from gait measurements. It is shown that the simulation results match those from gait measurements closely. These results suggest that the proposed model can provide a useful framework for analysis of postural control mechanisms.     

Stability switches and double Hopf bifurcation in a two-neural network system with multiple delays

Time delay is an inevitable factor in neural networks due to the finite propagation velocity and switching speed. Neural system may lose its stability even for very small delay. In this paper, a two-neural network system with the different types of delays involved in self- and neighbor- connection has been investigated. The local asymptotic stability of the equilibrium point is studied by analyzing the corresponding characteristic equation. It is found that the multiple delays can lead the system dynamic behavior to exhibit stability switches. The delay-dependent stability regions are illustrated in the delay-parameter plane, followed which the double Hopf bifurcation points can be obtained from the intersection points of the first and second Hopf bifurcation, i.e., the corresponding characteristic equation has two pairs of imaginary eigenvalues. Taking the delays as the bifurcation parameters, the classification and bifurcation sets are obtained in terms of the central manifold reduction and normal form method. The dynamical behavior of system may exhibit the quasi-periodic solutions due to the Neimark- Sacker bifurcation. Finally, numerical simulations are made to verify the theoretical results.     

Improved Power System Stability Using Backtracking Search Algorithm for Coordination Design of PSS and TCSC Damping Controller

Power system oscillation is a serious threat to the stability of multimachine power systems. The coordinated control of power system stabilizers (PSS) and thyristor-controlled series compensation (TCSC) damping controllers is a commonly used technique to provide the required damping over different modes of growing oscillations. However, their coordinated design is a complex multimodal optimization problem that is very hard to solve using traditional tuning techniques. In addition, several limitations of traditionally used techniques prevent the optimum design of coordinated controllers. In this paper, an alternate technique for robust damping over oscillation is presented using backtracking search algorithm (BSA). A 5-area 16-machine benchmark power system is considered to evaluate the design efficiency. The complete design process is conducted in a linear time-invariant (LTI) model of a power system. It includes the design formulation into a multi-objective function from the system eigenvalues. Later on, nonlinear time-domain simulations are used to compare the damping performances for different local and inter-area modes of power system oscillations. The performance of the BSA technique is compared against that of the popular particle swarm optimization (PSO) for coordinated design efficiency. Damping performances using different design techniques are compared in term of settling time and overshoot of oscillations. The results obtained verify that the BSA-based design improves the system stability significantly. The stability of the multimachine power system is improved by up to 74.47% and 79.93% for an inter-area mode and a local mode of oscillation, respectively. Thus, the proposed technique for coordinated design has great potential to improve power system stability and to maintain its secure operation.     

Study of a tri-trophic prey-dependent food chain model of interacting populations

The current paper accounts for the influence of intra-specific competition among predators in a prey dependent tri-trophic food chain model of interacting populations. We offer a detailed mathematical analysis of the proposed food chain model to illustrate some of the significant results that has arisen from the interplay of deterministic ecological phenomena and processes. Biologically feasible equilibria of the system are observed and the behaviours of the system around each of them are described. In particular, persistence, stability (local and global) and bifurcation (saddle-node, transcritical, Hopf–Andronov) analysis of this model are obtained. Relevant results from previous well known food chain models are compared with the current findings. Global stability analysis is also carried out by constructing appropriate Lyapunov functions. Numerical simulations show that the present system is capable enough to produce chaotic dynamics when the rate of self-interaction is very low. On the other hand such chaotic behaviour disappears for a certain value of the rate of self interaction. In addition, numerical simulations with experimented parameters values confirm the analytical results and shows that intra-specific competitions bears a potential role in controlling the chaotic dynamics of the system; and thus the role of self interactions in food chain model is illustrated first time. Finally, a discussion of the ecological applications of the analytical and numerical findings concludes the paper.     

Stage-structured cannibalism with delay in maturation and harvesting of an adult predator

A three-dimensional stage-structured predator–prey model is proposed and analyzed to study the effect of predation and cannibalism of the organisms at the highest trophic level with non-constant harvesting. Time lag in maturation of the predator is introduced in the system and conditions for local asymptotic stability of steady states are derived. The length of the delay preserving the stability is also estimated. Moreover, it is shown that the system undergoes a supercritical Hopf bifurcation when the maturation time lag crosses a certain critical value. Computer simulations have been carried out to illustrate various analytical results.     

Grazing weakens temporal stabilizing effects of diversity in the Eurasian steppe

Many biodiversity experiments have demonstrated that plant diversity can stabilize productivity in experimental grasslands. However, less is known about how diversity–stability relationships are mediated by grazing. Grazing is known for causing species losses, but its effects on plant functional groups (PFGs) composition and species asynchrony, which are closely correlated with ecosystem stability, remain unclear. We conducted a six‐year grazing experiment in a semi‐arid steppe, using seven levels of grazing intensity (0, 1.5, 3.0, 4.5, 6.0, 7.5, and 9.0 sheep per hectare) and two grazing systems (i.e., a traditional, continuous grazing system during the growing period (TGS), and a mixed one rotating grazing and mowing annually (MGS)), to examine the effects of grazing system and grazing intensity on the abundance and composition of PFGs and diversity–stability relationships. Ecosystem stability was similar between mixed and continuous grazing treatments. However, within the two grazing systems, stability was maintained through different pathways, that is, along with grazing intensity, persistence biomass variations in MGS, and compensatory interactions of PFGs in their biomass variations in TGS. Ecosystem temporal stability was not decreased by species loss but rather remain unchanged by the strong compensatory effects between PFGs, or a higher grazing‐induced decrease in species asynchrony at higher diversity, and a higher grazing‐induced increase in the temporal variation of productivity in diverse communities. Ecosystem stability of aboveground net primary production was not related to species richness in both grazing systems. High grazing intensity weakened the temporal stabilizing effects of diversity in this semi‐arid grassland. Our results demonstrate that the productivity of dominant PFGs is more important than species richness for maximizing stability in this system. This study distinguishes grazing intensity and grazing system from diversity effects on the temporal stability, highlighting the need to better understand how grazing regulates ecosystem stability, plant diversity, and their synergic relationships.     

Wavelength selection mechanism in the Gierer-Meinhardt model

We apply the concept of marginal stability hypothesis, which has been proposed for solving the problem of dendritic crystal growth, to the pattern selection problem in the Gierer-Meinhardt models. In the case of a large system, the system selects a definite wavelength of the ultimate spatial pattern when the unstable homogeneous steady state is locally disturbed. The numerical results are analyzed theoretically by means of the marginal stability hypothesis, and they are in good agreement with it. Biologically, these results imply why for large systems the Gierer-Meinhardt model (and presumably other reaction-diffusion schemes) have the ability to explain the observation that pattern-generating mechanisms are remarkably insensitive to a wide range of environmental and experimental conditions.     

一类带Monod增长率及脉冲状态反馈控制的微生物杀虫剂模型的周期解

研究了一类带Monod增长率及脉冲状态反馈控制的微生物杀虫剂模型．证明了无脉冲系统的负向全局渐近稳定性及带有脉冲状态反馈控制系统具有阶一周期解,并且给出阶一周期解存在和稳定的充分条件．数值模拟验证了理论结果．     

A robotic device for understanding neuromechanical interactions during standing balance control

Postural stability in standing balance results from the mechanics of body dynamics as well as active neural feedback control processes. Even when an animal or human has multiple legs on the ground, active neural regulation of balance is required. When the postural configuration, or stance, changes, such as when the feet are placed further apart, the mechanical stability of the organism changes, but the degree to which this alters the demands on neural feedback control for postural stability is unknown. We developed a robotic system that mimics the neuromechanical postural control system of a cat in response to lateral perturbations. This simple robotic system allows us to study the interactions between various parameters that contribute to postural stability and cannot be independently varied in biological systems. The robot is a 'planar', two-legged device that maintains compliant balance control in a variety of stance widths when subject to perturbations of the support surface, and in this sense reveals principles of lateral balance control that are also applicable to bipeds. Here we demonstrate that independent variations in either stance width or delayed neural feedback gains can have profound and often surprisingly detrimental effects on the postural stability of the system. Moreover, we show through experimentation and analysis that changing stance width alters fundamental mechanical relationships important in standing balance control and requires a coordinated adjustment of delayed feedback control to maintain postural stability.     

Rule Extraction Based on Extreme Learning Machine and an Improved Ant-Miner Algorithm for Transient Stability Assessment

In order to overcome the problems of poor understandability of the pattern recognition-based transient stability assessment (PRTSA) methods, a new rule extraction method based on extreme learning machine (ELM) and an improved Ant-miner (IAM) algorithm is presented in this paper. First, the basic principles of ELM and Ant-miner algorithm are respectively introduced. Then, based on the selected optimal feature subset, an example sample set is generated by the trained ELM-based PRTSA model. And finally, a set of classification rules are obtained by IAM algorithm to replace the original ELM network. The novelty of this proposal is that transient stability rules are extracted from an example sample set generated by the trained ELM-based transient stability assessment model by using IAM algorithm. The effectiveness of the proposed method is shown by the application results on the New England 39-bus power system and a practical power system — the southern power system of Hebei province.