Search

We explore the dynamics of a three-species Lotka-Volterra model incorporating intraguild (IG) predation. The model encompasses interactions between a basal prey, intraguild prey and omnivorous top/intraguild predator. These interactions are characterized by linear functional responses, while considering intraspecific competition and cooperative hunting dynamics. The study involves a comprehensive stability of different steady states and bifurcation analysis. Bifurcation structures unveil shifts in equilibrium stability and the emergence of new equilibrium states. Investigation into dynamics around the coexistence equilibrium highlights diverse behaviors, including stable coexistence, oscillations and chaos. Furthermore, exploration of species' densities under parameter variations uncovers distinct patterns, ranging from stability to chaos. Incorporating the concept of hunting cooperation among IG predators and IG prey can lead to the emergence or suppression of chaotic oscillations, respectively. Additionally, we observe that lower consumption rate of IG predator and cooperation of IG predator helps the system to keep in a stable state position. [ABSTRACT FROM AUTHOR]

In the present article, we set the if and only if conditions for the solutions of the class of neutral impulsive delay second-order differential equations. We consider two cases when it is non-increasing and non-decreasing for quotient of two positive odd integers. Our main tool is the Lebesgue's dominated convergence theorem. Examples illustrating the applicability of the results are also given, and state an open problem. [ABSTRACT FROM AUTHOR]

In this paper, necessary and sufficient conditions are establish of the solutions to second-order delay differential equations of the form (r(t)(x′(t))λ)′ + ∑i=1m qi (t) fi (x(σi(t))) = 0 for t ≥ t0, We consider two cases when fi(u)/uβ is non-increasing for β < γ, and non-decreasing for β > γ where β and γ are the quotient of two positive odd integers. Our main tool is Lebesgue's Dominated Convergence theorem. Examples illustrating the applicability of the results are also given, and state an open problem. [ABSTRACT FROM AUTHOR]

This work provides new adequate conditions for difference equations with forcing, positive and negative terms to have non-oscillatory solutions. A few mathematical inequalities and the properties of discrete fractional calculus serve as the fundamental foundation to our approach. To help establish the main results, an analogous representation for the main equation, called a Volterra-type summation equation, is constructed. Two numerical examples are provided to demonstrate the validity of the theoretical findings; no earlier publications have been able to comment on their solutions' non-oscillatory behavior. [ABSTRACT FROM AUTHOR]

The investigation on the oscillatory and asymptotic properties of differential equations plays an important role in many applications, such as engineering, physics and medicine. In this work, we establish some new sufficient conditions for both the oscillatory and asymptotic behavior of the solutions to a second-order neutral impulsive differential system (IDS, for short) with deviating argument and fixed moments of impulse effect under both canonical and non-canonical operators with various values of the neutral coefficient. Also, we obtain the condition for the existence of a positive solution of the system under consideration. Finally, two examples are provided to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this work, we obtain necessary and sufficient conditions for oscillation of solutions of second-order neutral impulsive differential system... . . ., where z(t) = x(t) + p(t)x(τ (t)). Under the assumption ∫∞0 r(η)-1/γ dη = ∞, we consider two cases when γ > αi and γ < αi. Our main tool is Lebesgue's Dominated Convergence theorem. Examples are given to illustrate our main results and we state an open problem. [ABSTRACT FROM AUTHOR]

In this work, we obtain necessary and sufficient conditions for the oscillation of solutions of a second‐order neutral differential equation with impulses. Two examples are provided to show the effectiveness and feasibility of the main results. Our main tool is the Lebesgue's Dominated Convergence theorem. [ABSTRACT FROM AUTHOR]