جستجوی مقالات مرتبط با کلیدواژه « periodic solution » در نشریات گروه « ریاضی »
تکرار جستجوی کلیدواژه «periodic solution» در نشریات گروه «علوم پایه»-
We consider a planar symmetric vector field that undergoes a homoclinic bifurcation. In order to study the existence of exterior periodic solutions of the vector field around broken symmetric homoclinic orbits, we investigate the existence of fixed points of the exterior Poincare map around these orbits. This Poincare map is the result of the combination of flows inside and outside the homoclinic orbits. It shows how a big periodic orbit converts to two small periodic orbits by passing through a double homoclinic structure. Finally, we use the results to investigate the existence of periodic solutions of the perturbed Duffing equation.
Keywords: Poincare map, homoclinic bifurcation, fixed point, periodic solution} -
Some existence and uniqueness results of a houseflies model with a delay depending on time and stateInternational Journal Of Nonlinear Analysis And Applications, Volume:14 Issue: 1, Jan 2023, PP 865 -876This work elucidates the sufficient conditions for establishing some existence and uniqueness results for a Musca Domestica model that is governed by a first-order nonlinear differential equation with iterative terms resulting from a time and state-dependent delay. The existence of at least one positive periodic solution is proved by using Schauder's fixed point theorem with the help of some properties of an obtained Green's function. Furthermore, under an additional condition, the Banach contraction principle is applied to guarantee the existence, uniqueness and stability of solutions. Finally, the validity of our main findings is demonstrated by two examples. Our findings are completely new and generalize previous ones to some degree.Keywords: Delay Differential Equation, Fixed point theorem, Green's function, Periodic solution, positive solution}
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International Journal Of Nonlinear Analysis And Applications, Volume:13 Issue: 1, Winter-Spring 2022, PP 1462 -1478
In this work, we are interested in the study of the limit cycles of a perturbed differential system in R2, given as follows \left\{ \begin{array}{l} \dot{x}=y, \\ \dot{y}=-x-\varepsilon (1+\sin ^{m}(\theta ))\psi (x,y),% \end{array}% \right. where ε is small enough, m is a non-negative integer, tan(θ)=y/x, and ψ(x,y) is a real polynomial of degree n≥1. We use the averaging theory of first-order to provide an upper bound for the maximum number of limit cycles. In the end, we present some numerical examples to illustrate the theoretical results.
Keywords: Periodic solution, averaging method, differential system} -
In this paper, we present a detailed study of the following difference equation xn+1 = αn 1 + xnxn−1 , n ∈ N0, where the sequence (αn)n≥0 is positive, real, periodic with period two and the initial values x−1, x0 are nonnegative real numbers. By this study, we determine global behavior of p
Keywords: Closed form solution, difference equations, global behavior, periodic solution, periodic coefficients} -
We prove the existence of solutions for the neutral periodic integro-differential equation with infinite delay x 0 (t) = G(t, x(t), x(t − τ (t))) + d dtQ(t, x(t − τ (t))) + Z t −∞ Xn j=1 gj (t, s) f(x(s))ds, x(t + T) = x(t). A Krasnoselskii and Banach’s fixed point theorems are employed in establishing our results.
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Keywords: Krasnoselskii's Fixed point theorem, integro-differential neutral equation, periodic solution} -
ýIn this paperý, ýfirst we discuss a local stability analysis of model was introduced by Pý. ýJý. ýMumby etý. ýalý. ý(2007)ý, ýwith $\frac{gM^{2}}{M}$ as the functional response termý. ýWe conclude that the grazing intensity is the important parameter to control the existence or extinction of the coral reefý. ýNextý, ýwe consider this model under the influence of the time delay as the bifurcation parameterý. ýWe show that for small time delayý, ýthe stability type of the equilibria will not changeý, ýhowever for large enough time delayý, ýthe interior equilibrium point become unstable in contrast to the ODE caseý. ýAlso for some critical grazing intensity and the time delayý, ýa Hopf bifurcation occur and a nontrivial periodic orbit will appearý. ýFurther we discuss its corresponding stability switching directionsý.Keywords: Ordinary differential equation, Delay differential equation, Stability, Hopf bifurcation, periodic solution}
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In this paper, sufficient conditions are investigated for the existence of periodic (not necessarily positive) solutions for nonlinear several time delay population system with feedback control. Nonlinear system affected by an periodic external source is studied. Existence of a control variable provides the extension of some previous results obtained in other studies. We give a illustrative example in order to indicate the validity of the assumptions.Keywords: Schauder's fixed, point theorem, Periodic solution, Population equation, Feedback control}
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Iranian Journal of Numerical Analysis and Optimization, Volume:4 Issue: 2, Summer and Autumn 2014, PP 15 -30In this paper, we consider a general ring network consisting of n neurons and n time delays. By analyzing the associated characteristic equation, a classification according to n is presented. It is investigated that Hopf bifur-cation occurs when the sum of the n delays passes through a critical value.In fact, a family of periodic solutions bifurcate from the origin, while the zero solution loses its asymptotically stability. To illustrate our theoretical results, numerical simulation is given.Keywords: Ring network, Stability, Periodic solution, Hopf bifurcation, Time delay}
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The existence and uniqueness of a periodic solution of the system of differential equations d dtx(t) = A(t)x(t − τ ) are proved. In particular the Krasnoselskii’s fixed point theorem and the contraction mapping principle are used in the analysis. In addition, the notion of fundamental matrix solution coupled with Floquet theory is also employed.
Keywords: Fixed point, Fundamental matrix solution, Floquet theory, Periodic solution} -
In the present paper the linear oscillator in R3 with z =constant has been considered. The aim is to determine the necessary conditions for the persistence of periodic solutions under discontinuous perturbations. A new approach based on a computational method has been used. At the end we apply our method on an example.Keywords: Perturbation, Periodic solution, Discontinuous system}
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In this paper, we will consider third order linear differential equation y 000 + αy00 + βy0 + γy + f(t, y) = e(t), where α, β, γ are constant coefficients, f(t, y) is continuous, e(t) is discontinuous, and f and e are periodic functions with respect to t of period w. We will introduce sufficient conditions under which the above equation have at least one non-trivial periodic solution of period w. We will see that under the so called conditions, all the solutions of the equation will be bounded. It must be mentioned that e in this equation is called “controller” in the engineering problems and it was always considered to be continuous to ensure us that periodic solution exists. In this paper, we will show the existence of periodic solution without supposing that e to be continuous
Keywords: Periodic solution, linear third orderODE, bounded solution, stability, discontinuous controller}
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