Hopf bifurcation analysis of coupled two-neuron system with discrete and distributed delays

Karaoğlu, Esra; Yılmaz, Enes; Merdan, H.

doi:10.1007/s11071-016-2742-0

Cited by 12 publications

(11 citation statements)

References 26 publications

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“…In recent decades, the analysis of the effect of investment delay has been the focus of extensive examination as a tool for endogenous cycles to explain business cycles and growth cycles. Differential equations with time delay (discrete or distributed) and their mathematical methods have been seen to be the most adequate tools to model the business cycle and growth in an economy where the investment delay plays a cru-cial role [1][2][3][4][5], as well as in physics, finance and biology [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Bifurcations in an economic growth model with a distributed time delay transformed to ODE

2020

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In this paper, we consider a model of economic growth with a distributed time-delay investment function, where the time-delay parameter is a mean time delay of the gamma distribution. Using the linear chain trick technique, we transform the delay differential equation system into an equivalent one of ordinary differential equations (ODEs). Since we are dealing with weak and strong kernels, our system will be reduced to a three-and four-dimensional ODE system, respectively. The occurrence of Hopf bifurcation is investigated with respect to the following two parameters: time-delay parameter and rate of growth parameter. Sufficient criteria on the existence and stability of a limit cycle solution through the Hopf bifurcation are presented in case of time-delay parameter. Numerical studies with the Dana and Malgrange investment

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Section: Introductionmentioning

confidence: 99%

Bifurcations in an economic growth model with a distributed time delay transformed to ODE

2020

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“…For the above simulations we consider interesting for further investigation the study of both mixed system, in particular the analysis of all possible bifurcation should be performed in the future. Moreover, in the previous simulations we have only considered the case m = 1 ( as done for example in [6], [7]), while in many cases (see for example [16,15,14]) the values of m may change the qualitative behaviour of the system. In any case, the mixed delay case (both constant and distributed) is able to recover the complex behaviour observed in the constant delay case.…”

Section: Case M = 2 Equation (21) Becomesmentioning

confidence: 99%

Bifurcation scenarios in an ordinary differential equation with constant and distributed delay: A case study

Caraballo¹,

Colucci²,

Guerrini³

2019

Discrete &Amp; Continuous Dynamical Systems - B

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In this article we consider a model introduced by Ucar in order to simply describe chaotic behaviour with a one dimensional ODE containing a constant delay. We study the bifurcation problem of the equilibria and we obtain an approximation of the periodic orbits generated by the Hopf bifurcation. Moreover, we propose and analyse a more general model containing distributed time delay. Finally, we propose some ideas for further study. All the theoretical results are supported and illustrated by numerical simulations.

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“…In order to grasp the impact of the distributed delay on Hopf bifurcation for neural networks concerning time delay, plenty of authors have dedicated themselves to all kinds of neural networks involving distributed delays (see [27,28]). In 2016, Karaoglu et al [29] analyzed the following neural networks concerning mixed delays:…”

Section: Introductionmentioning

confidence: 99%

“…In [29], Karaoglu et al took kernel function as case (2). By means of stability criterion and Hopf bifurcation theory of delayed differential equation, Karaoglu et al obtained a sufficient condition to guarantee the stability and the onset of Hopf bifurcation of system (1).…”

Section: Introductionmentioning

confidence: 99%

Periodic Oscillatory Phenomenon in Fractional-Order Neural Networks Involving Different Types of Delays

Wang

Liu

2021

Mathematical Problems in Engineering

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This research is chiefly concerned with the stability and Hopf bifurcation for newly established fractional-order neural networks involving different types of delays. By means of an appropriate variable substitution, equivalent fractional-order neural network systems involving one delay are built. By discussing the distribution of roots of the characteristic equation of the established fractional-order neural network systems and selecting the delay as bifurcation parameter, a novel delay-independent bifurcation condition is derived. The investigation verifies that the delay is a significant parameter which has an important influence on stability nature and Hopf bifurcation behavior of neural network systems. The computer simulation plots and bifurcation graphs effectively illustrate the reasonableness of the theoretical fruits.

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Hopf bifurcation analysis of coupled two-neuron system with discrete and distributed delays

Cited by 12 publications

References 26 publications

Bifurcations in an economic growth model with a distributed time delay transformed to ODE

Bifurcations in an economic growth model with a distributed time delay transformed to ODE

Bifurcation scenarios in an ordinary differential equation with constant and distributed delay: A case study

Periodic Oscillatory Phenomenon in Fractional-Order Neural Networks Involving Different Types of Delays

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