Considered is a system of delay differential equations modeling a time-delayed connecting network of three neurons without self-feedback.
Linear stability and Hopf bifurcation in a two-neuron network with three delays (one is due to the self-feedback) are investigated.
Apr 30, 2024 · Linear stability and Hopf bifurcation in a two-neuron network with three delays (one is due to the self-feedback) are investigated.
Semantic Scholar extracted view of "Linear stability and Hopf bifurcation in a three-unit neural network with two delays" by Shaofen Zou et al.
Considered is a system of delay differential equations modeling a time-delayed connecting network of three neurons without self-feedback.
(3) undergoes a Hopf bifurcation which is supercritical and the bifurcating periodic solutions are orbitally asymptotically stable. Numerical simulations ...
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Abstract. A neural network model with three neurons and a single time delay is considered. Its linear stability is investigated and Hopf bifurcations are ...
People also ask
What is the direction and stability of Hopf bifurcation?
Direction and Stability of the Hopf Bifurcation
In Theorem 2, we obtained a condition under which system (2) undergoes Hopf bifurcation at τ0; that is, a family of periodic solutions bifurcate from the positive steady state point (K∗, L∗) at the critical value τ0.
What causes Hopf bifurcation?
In a differential equation a Hopf bifurcation typically occurs when a complex conjugate pair of eigenvalues of the linearised flow at a fixed point becomes purely imaginary. This implies that a Hopf bifurcation can only occur in systems of dimension two or higher.
What is limit cycle and Hopf bifurcation?
A Hopf Bifurcation occurs when a periodic solution or limit cycle, surrounding an equilibrium point, arises or goes away as a parameter µ varies. When a stable limit cycle surrounds an unstable equilibrium point, the bifurcation is called a supercritical Hopf bifurcation.
How to find Hopf bifurcation?
You can check whether the bifurcation is Hopf or not by looking at the imaginary components of the dominant eigenvalues whose real parts are at a critical value (zero); if there are non-zero imaginary components, it must be a Hopf bifurcation. Re(λ)={r±√r2−42if r2≥4,orr2if r2<4.
Its dynamics is investigated in term of the linear stability analysis and Hopf bifurcation analysis. By regarding the sum of two delays as a bifurcation ...
Linear stability and Hopf bifurcation in a three-unit neural network with two delays. Neurocomputing, Vol. 70, No. 1-3 | 1 Dec 2006. A PERTURBATION ...
In this paper, a bidirectional associative memory NN with four neurons and multiple delays is considered. By applying the normal form theory and the center ...