PERMANENCE FOR THE LOTKA–VOLTERRA COOPERATIVE SYSTEM WITH SEVERAL DELAYS

2009 ◽  
Vol 02 (03) ◽  
pp. 267-285 ◽  
Author(s):  
YUKIHIKO NAKATA
Keyword(s):  
Theoretical Analysis ◽  
Time Delays ◽  
Interspecific Interactions ◽  
Cooperative Systems ◽  
Numerical Results ◽  
Sufficient Condition ◽  
Cooperative System ◽  
Nonlinear Anal ◽  
Discrete Delays ◽  
Several Delays

In this paper, we establish a new sufficient condition of the permanence for the Lotka–Volterra cooperative systems with multiple discrete delays by extending the results in [Nakata and Muroya, Permanence for nonautonomous Lotka–Volterra cooperative systems with delays, Nonlinear Anal. RWA., in press]. Our condition holds even if the instantaneous feedback does not dominate over the total of the interspecific interactions and does not need the restriction on the size of time delays, different from the results in [Lu and Lu, Permanence for two-species Lotka–Volterra cooperative systems with delays, Math. Biosci. Eng.5 (2008) 477–484]. We offer an example for comparison with the previous results and numerical results supporting our theoretical analysis are given.

scholarly journals Distinct Spreading Speeds in a Lotka–Volterra Cooperative System

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Shuxia Pan
Keyword(s):  
Level Sets ◽  
Numerical Results ◽  
Sufficient Condition ◽  
Cooperative System ◽  
Spreading Speeds ◽  
Upper Solution ◽  
Constant Coefficients

This paper deals with the spreading speeds in the classical Lotka–Volterra cooperative system, of which the bounds have been studied earlier. By introducing an auxiliary cooperative system and constructing an upper solution, we obtain a sufficient condition to confirm two distinct spreading speeds of unknown functions. Due to the different average moving speeds of different level sets, we find the existence of propagation terraces in such a cooperative system with constant coefficients. We also present some numerical results to illustrate our results.

scholarly journals Stability of a Three-Species Cooperative System with Time Delays and Stochastic Perturbations

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Jinxing Zhao ◽  
Yuanfu Shao
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
System Dynamics ◽  
Numerical Simulations ◽  
Time Delays ◽  
Cooperative Systems ◽  
Asymptotical Stability ◽  
Cooperative System ◽  
Stochastic Perturbations ◽  
Stability In Probability

Considering the impacts of time delays and different kinds of stochastic perturbations, we propose two three-species delayed cooperative systems with stochastic perturbations in this paper. We establish the sufficient criteria of the asymptotical stability and stability in probability by constructing a neutral stochastic differential equation and some suitable functionals. The impacts of time delays and stochastic perturbations to the system dynamics are revealed by some numerical simulations at the end.

scholarly journals Numerical methods for solving the multi-term time-fractional wave-diffusion equation

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Fawang Liu ◽  
Mark Meerschaert ◽  
Robert McGough ◽  
Pinghui Zhuang ◽  
Qingxia Liu
Keyword(s):  
Numerical Methods ◽  
Theoretical Analysis ◽  
Diffusion Equation ◽  
Fractional Derivatives ◽  
Fractional Laplacian ◽  
Numerical Results ◽  
Diffusion Equations ◽  
Time Space ◽  
Methods And Techniques ◽  
Wave Diffusion

AbstractIn this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

Modulus-based Synchronous Multisplitting Iteration Methods for an Implicit Complementarity Problem

2017 ◽  
Vol 7 (2) ◽  
pp. 363-375 ◽  
Author(s):  
Chen-Liang Li ◽  
Jun-Tao Hong
Keyword(s):  
Theoretical Analysis ◽  
Complementarity Problem ◽  
Numerical Results ◽  
Multiprocessor Systems ◽  
Implicit Complementarity Problem ◽  
New Methods ◽  
Iteration Methods

AbstractWe construct modulus-based synchronous multisplitting iteration methods to solve a large implicit complementarity problem on parallel multiprocessor systems, and prove their convergence. Numerical results confirm our theoretical analysis and show that these new methods are efficient.

AN ASYMPTOTIC STABILITY THEOREM FOR QUASILINEAR DELAY DIFFERENTIAL EQUATIONS WITH OSCILLATING COEFFICIENTS

2013 ◽  
Vol 24 (11) ◽  
pp. 1350092 ◽  
Author(s):  
NGUYEN TIEN DUNG
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Asymptotic Behavior Of Solutions ◽  
Variable Delays ◽  
Nonlinear Anal ◽  
Oscillating Coefficients ◽  
Several Delays

In this paper, we provide new necessary and sufficient conditions of the asymptotic stability for a class of quasilinear differential equations with several delays and oscillating coefficients. Our results are established by means of fixed point theory and improve those obtained in [J. R. Graef, C. Qian and B. Zhang, Asymptotic behavior of solutions of differential equations with variable delays, Proc. London Math. Soc.81 (2000) 72–92; B. Zhang, Fixed points and stability in differential equations with variable delays, Nonlinear Anal.63 (2005) e233–e242].

Exponential lag function projective synchronization of memristor-based multidirectional associative memory neural networks via hybrid control

2018 ◽  
Vol 32 (09) ◽  
pp. 1850116 ◽  
Author(s):  
Manman Yuan ◽  
Weiping Wang ◽  
Xiong Luo ◽  
Lixiang Li ◽  
Jürgen Kurths ◽  
...  
Keyword(s):  
Neural Networks ◽  
Associative Memory ◽  
Time Delays ◽  
Hybrid Control ◽  
Projective Synchronization ◽  
Mixed Delays ◽  
Time Varying ◽  
Function Projective Synchronization ◽  
Different Types ◽  
Discrete Delays

This paper is concerned with the exponential lag function projective synchronization of memristive multidirectional associative memory neural networks (MMAMNNs). First, we propose a new model of MMAMNNs with mixed time-varying delays. In the proposed approach, the mixed delays include time-varying discrete delays and distributed time delays. Second, we design two kinds of hybrid controllers. Traditional control methods lack the capability of reflecting variable synaptic weights. In this paper, the controllers are carefully designed to confirm the process of different types of synchronization in the MMAMNNs. Third, sufficient criteria guaranteeing the synchronization of system are derived based on the derive-response concept. Finally, the effectiveness of the proposed mechanism is validated with numerical experiments.

scholarly journals Stabilization of a Class of Switched Positive Nonlinear Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Xing Xing ◽  
Zhichun Jia ◽  
Yunfei Yin ◽  
Tingting Wu
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Dwell Time ◽  
Average Dwell Time ◽  
Sufficient Condition ◽  
Cooperative System ◽  
Numerical Example ◽  
New Class

The problem of switching stabilization for a class of switched positive nonlinear systems (switched positive homogeneous cooperative system (SPHCS) in the continuous-time context and switched positive homogeneous order-preserving system (SPHOS) in the discrete-time context) is studied by using average dwell time (ADT) approach, where the positive subsystems are possibly all unstable. To tackle this problem, a new class of ADT switching is first defined, which is different from the previous defined ADT switching in the literature. Then, the proposed ADT is designed via analyzing the weightedl∞norm of the considered system’s state. A sufficient condition of stabilization for SPHCSs with unstable positive subsystems is derived in continuous-time context. Furthermore, a sufficient condition for SPHOSs under the assumption that all modes are possibly unstable is also obtained. Finally, a numerical example is given to demonstrate the advantages and effectiveness of our developed results.

scholarly journals Global Behavior of a Computer Virus Propagation Model on Multilayer Networks

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Chunming Zhang
Keyword(s):  
Theoretical Analysis ◽  
Computer Virus ◽  
Propagation Model ◽  
Global Behavior ◽  
Sufficient Condition ◽  
Multilayer Networks ◽  
Virus Propagation ◽  
Simulation Results ◽  
Computer Virus Propagation Model ◽  
Vital Factor

This paper presents a new linear computer viruses propagation model on multilayer networks to explore the mechanism of computer virus propagation. Theoretical analysis demonstrates that the maximum eigenvalue of the sum of all the subnetworks is a vital factor in determining the viral prevalence. And then, a new sufficient condition for the global stability of virus-free equilibrium has been obtained. The persistence of computer virus propagation system has also been proved. Eventually, some numerical simulation results verify the main conclusions of the theoretical analysis.

Cooperative Robots

2015 ◽  
pp. 30-91
Author(s):  
Pablo Sánchez-Sánchez ◽  
Marco A. Arteaga-Pérez
Keyword(s):  
Path Planning ◽  
Dynamic Model ◽  
Cooperative Systems ◽  
Projection Matrix ◽  
Cooperative System ◽  
Cooperative Robots ◽  
Contact Tasks

The interest in developing cooperative systems has increased due to the advantages they offer. Such systems can perform tasks that a single robot would be impossible to achieve. In this chapter, a summary of the cooperative robots's study, a classification of the type of grips, and path planning is presented. In addition, the properties and characteristics of the dynamic model, and the effects of torque and friction in contact tasks are shown. General considerations that should be made to analyze a cooperative system are introduced, and finally, the principle of orthogonalization, which separates the position and the force using a projection matrix which allows us to develop a control-observer scheme, is presented.

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