Blowflies System Research Articles

Dynamics of Nicholson's blowflies system with spatial heterogeneity, nonlocal operator and delay

Dynamics of Nicholson's blowflies system with spatial heterogeneity, nonlocal operator and delay

Positive almost periodic solution for competitive and cooperative Nicholson's blowflies system

<abstract><p>In this paper, we investigate a class of competitive and cooperative Nicholson's blowfly equations. By applying the Lyapunov functional and analysis technique, the conditions for the existence and exponential convergence of a positive almost periodic solution are derived. Moreover, an example and numerical simulation for justifying the theoretical analysis are also provided.</p></abstract>

Novel Results on Persistence and Attractivity of Delayed Nicholson's Blowflies System with Patch Structure

This paper is concerned with the dynamic characteristics of a class of Nicholson's blowflies system with patch structure and multiple pairs of distinct time-varying delays. We aim to find the influence of the distinct time-varying delays in the same reproductive function on its asymptotic behavior. First, we derive the global existence, positiveness and uniform persistence of solutions for the addressed system. Then, by employing the theory of functional differential equations, the fluctuation lemma and the technique of differential inequalities, we build up some new delay-dependent criteria for the global attractivity of the positive equilibrium point vector, which does not possess the same components. In addition, we exam the effectiveness and feasibility of the theoretical achievements by some numerical simulations.

Stability on a patch-structured Nicholson's blowflies system incorporating mature delay and feedback delay

In this paper, we focus on a patch-structured Nicholson's blowflies system incorporating mature delay and feedback delay. First, by exploiting the differential inequality technique, fluctuation lemma and Brouwer fixed point theorem, we obtain the persistence and the existence of the positive equilibrium point with different components. Second, we develop an approach to establish some new criteria to guarantee the local stability and global attractivity of the positive equilibrium point vector, which complement and improve some existing results. Last, the effectiveness and feasibility of the theoretical results are illustrated by some computer simulations.

Convergence analysis of a patch structure Nicholson’s blowflies system involving an oscillating death rate

ABSTRACT This paper focuses on the convergence analysis for a patch structure Nicholson’s blowflies system involving an oscillating death rate and multiple different time-varying delays. By using inequality techniques and concise mathematical analysis proof, some sufficient criteria are established to guarantee the global exponential convergence of the zero equilibrium point for the addressed system. Our results are novel and supplement some existing ones. Furthermore, the effectiveness and feasibility of the obtained results are demonstrated by some numerical simulations.

Stability for patch structure Nicholson’s blowflies systems involving distinctive maturation and feedback delays

ABSTRACT This article explores a class of patch structure Nicholson’s blowflies systems involving nonlinear density-dependent mortality terms and multiple pairs of distinctive maturation and feedback delays. By utilising the fluctuation lemma and differential inequality techniques, a delay-dependent criterion on the global asymptotic stability of the addressed systems is established, which refines and complements some existing ones. In addition, the numerical simulations verify the efficacy and accuracy of the obtained findings.

Global asymptotic stability for a nonlinear density-dependent mortality Nicholson\u2019s blowflies system involving multiple pairs of time-varying delays

In our article, a nonlinear density-dependent mortality Nicholson’s blowflies system with patch structure has been investigated, in which the delays are time-varying and multiple pairs. Based upon the fluctuation lemma and differential inequality techniques, some sufficient conditions are found to ensure the global asymptotic stability of the addressed model. Moreover, a numerical example is provided to illustrate the feasibility and effectiveness of the obtained findings, and our consequences are new even when the considered model degenerates to the scalar Nicholson’s blowflies equation.

Stability on a patch structure Nicholson’s blowflies system involving distinctive delays

By introducing multiple pairs of different time-varying delays in the time-dependent birth functions, this paper proposes explores a patch structure Nicholson’s blowflies system involving distinctive delays. Without assuming the uniform positiveness of the dead rate and the boundedness of coefficients, the global stability of the considered system is established by employing some novel inequality techniques. The obtained results refine and complement some existing ones.

Novel stability criteria on nonlinear density-dependent mortality Nicholson\u2019s blowflies systems in asymptotically almost periodic environments

In this paper, we consider nonlinear density-dependent mortality Nicholson’s blowflies system involving patch structures and asymptotically almost periodic environments. By developing an approach based on differential inequality techniques coupled with the Lyapunov function method, some criteria are demonstrated to guarantee the global attractivity of the addressed systems. Finally, we give a numerical example to illustrate the effectiveness and feasibility of the obtain results.

Global convergence dynamics of almost periodic delay Nicholson's blowflies systems

We take into account nonlinear density-dependent mortality term and patch structure to deal with the global convergence dynamics of almost periodic delay Nicholson's blowflies system in this paper. To begin with, we prove that the solutions of the addressed system exist globally and are bounded above. What's more, by the methods of Lyapunov function and analytical techniques, we establish new criteria to check the existence and global attractivity of the positive asymptotically almost periodic solution. In the end, we arrange an example to illustrate the effectiveness and feasibility of the obtained results.

Periodicity on Nicholson’s blowflies systems involving patch structure and mortality terms

ABSTRACTIn this paper, we investigate a class of delayed Nicholson’s blowflies systems with patch structure and nonlinear density-dependent mortality terms. By using differential inequality approach and Lyapunov function method, some criteria are established for the existence, uniqueness and exponential stability of positive periodic solutions for the addressed systems. Finally, we give a numerical example to illustrate the effectiveness and feasibility of the obtain results.

GLOBAL EXPONENTIAL STABILITY OF ALMOST PERIODIC SOLUTIONS FOR NICHOLSON’S BLOWFLIES SYSTEM WITH NONLINEAR DENSITY-DEPENDENT MORTALITY TERMS AND PATCH STRUCTURE

This paper considers a generalized Nicholson’s blowflies system with nonlinear density-dependent mortality terms and patch structure. Under appropriate conditions, we establish some criteria to ensure that the solutions of this system exist and converge globally exponentially to a positive almost periodic solution. The results complement another case of nonlinear density-dependent mortality terms in Chen and Wang [5].

Exponential extinction of discrete Nicholson's blowflies systems with patch structure and mortality terms

Exponential extinction of discrete Nicholson's blowflies systems with patch structure and mortality terms

Neimark-Sacker bifurcation analysis in a discrete neutral Nicholson’s blowflies system with delay

In this paper, we investigate the Neimark-Sacker bifurcation in a delayed Nicholson’s blowflies system of neutral type, which is obtained by using Euler discretization method. Choosing time delay as the bifurcation parameter and analysing the associated characteristic equation, we study the stability of the positive equilibrium and verify the existence of the Neimark-Sacker bifurcation. Then, an explicit formula which determines the stability and direction of the bifurcation is given by using centre manifold theorem and normal form theory. Finally, some numerical simulations are given to illustrate our theoretical results.

Almost periodic solutions for a delayed Nicholson’s blowflies system with nonlinear density-dependent mortality terms and patch structure

We study positive almost periodic solutions for a delayed Nicholson’s blowflies system with nonlinear density-dependent mortality terms and patch structure. By applying the differential inequality technique and the Lyapunov functional, we derive sufficient conditions for the existence and global exponential stability of positive almost periodic solutions. We also give an example and its numerical simulations to support the theoretical effectiveness.

Persistence, Permanence and Global Stability for an $$n$$ n -Dimensional Nicholson System

For a Nicholson's blowflies system with patch structure and multiple discrete delays, we analyze several features of the global asymptotic behavior of its solutions. It is shown that if the spectral bound of the community matrix is non-positive, then the population becomes extinct on each patch, whereas the total population uniformly persists if the spectral bound is positive. Explicit uniform lower and upper bounds for the asymptotic behavior of solutions are also given. When the population uniformly persists, the existence of a unique positive equilibrium is established, as well as a sharp criterion for its absolute global asymptotic stability, improving results in the recent literature. While our system is not cooperative, several sharp threshold-type results about its dynamics are proven, even when the community matrix is reducible, a case usually not treated in the literature.

Exponential Extinction of Nicholson′s Blowflies System with Nonlinear Density‐Dependent Mortality Terms

This paper presents a new generalized Nicholson’s blowflies system with patch structure and nonlinear density‐dependent mortality terms. Under appropriate conditions, we establish some criteria to guarantee the exponential extinction of this system. Moreover, we give two examples and numerical simulations to demonstrate our main results.

Traveling wave fronts in reaction-diffusion systems with spatio-temporal delay and applications

This paper is concerned with monotone traveling wave solutions of reaction-diffusion systems with spatio-temporal delay. Our approach is to use a new monotone iteration scheme based on a lower solution in the set of the profiles. The smoothness of upper and lower solutions is not required in this paper. We will apply our results to Nicholson's blowflies systems with non-monotone birth functions and show that the systems admit traveling wave solutions connecting two spatially homogeneous equilibria and the wave shape is monotone. Due to the biological realism, the positivity of the monotone traveling wave solutions can be directly obtained by the construction of suitable upper-lower solutions.