456 research outputs found
Persistence and Global Stability in a Population Model
AbstractA difference equation modelling the dynamics of a population undergoing a density-dependent harvesting is considered. A sufficient condition is established for all positive solutions of the corresponding discrete dynamic system to converge eventually to the positive equilibrium. Elementary methods of differential calculus are used. The result of this article provides a generalization of a result known for a simpler special model with no harvesting
Oscillations of delay differential equations
[Mathematical equations cannot be displayed here, refer to PDF
Hopf Bifurcation and Chaos in Tabu Learning Neuron Models
In this paper, we consider the nonlinear dynamical behaviors of some tabu
leaning neuron models. We first consider a tabu learning single neuron model.
By choosing the memory decay rate as a bifurcation parameter, we prove that
Hopf bifurcation occurs in the neuron. The stability of the bifurcating
periodic solutions and the direction of the Hopf bifurcation are determined by
applying the normal form theory. We give a numerical example to verify the
theoretical analysis. Then, we demonstrate the chaotic behavior in such a
neuron with sinusoidal external input, via computer simulations. Finally, we
study the chaotic behaviors in tabu learning two-neuron models, with linear and
quadratic proximity functions respectively.Comment: 14 pages, 13 figures, Accepted by International Journal of
Bifurcation and Chao
N-[4-(2-Morpholinoethoxy)phenyl]acetamide monohydrate
In the title compound, C14H20N2O3·H2O, the geometry about the morpholine N atom implies sp
3 hybridization. In the crystal, symmetry-related molecules are linked by intermolecular N—H⋯O, O—H⋯O and O—H⋯N hydrogen bonds, forming infinite chains along the b axis. The chain structure is further stabilized by intramolecular C—H⋯O interactions
Synchronization in a neuronal feedback loop through asymmetric temporal delays
We consider the effect of asymmetric temporal delays in a system of two
coupled Hopfield neurons. For couplings of opposite signs, a limit cycle
emerges via a supercritical Hopf bifurcation when the sum of the delays reaches
a critical value. We show that the angular frequency of the limit cycle is
independent of an asymmetry in the delays. However, the delay asymmetry
determines the phase difference between the periodic activities of the two
components. Specifically, when the connection with negative coupling has a
delay much larger than the delay for the positive coupling, the system
approaches in-phase synchrony between the two components. Employing variational
perturbation theory (VPT), we achieve an approximate analytical evaluation of
the phase shift, in good agreement with numerical results.Comment: 5 pages, 4 figure
Characteristics of a Delayed System with Time-dependent Delay Time
The characteristics of a time-delayed system with time-dependent delay time
is investigated. We demonstrate the nonlinearity characteristics of the
time-delayed system are significantly changed depending on the properties of
time-dependent delay time and especially that the reconstructed phase
trajectory of the system is not collapsed into simple manifold, differently
from the delayed system with fixed delay time. We discuss the possibility of a
phase space reconstruction and its applications.Comment: 4 pages, 6 figures (to be published in Phys. Rev. E
4-[2-(4-Methoxyphenyl)ethyl]-3-(thiophen-2-ylmethyl)-1H-1,2,4-triazol-5(4H)-one monohydrate
In the title compound, C16H17N3O2S·H2O, the triazole ring makes a dihedral angle of 34.63 (6)° with the benzene ring. The thiophene ring is disordered over two orientations [occupancy ratio = 0.634 (4):0.366 (4)] which make dihedral angles of 54.61 (16) and 54.57 (31)° with the triazole ring. Intermolecular N—H⋯O and O—H⋯O hydrogen bonds stabilize the crystal structure
Exact synchronization bound for coupled time-delay systems
We obtain an exact bound for synchronization in coupled time-delay systems using the generalized Halanay inequality for the general case of time-dependent delay, coupling, and coefficients. Furthermore, we show that the same analysis is applicable to both uni- and bidirectionally coupled time-delay systems with an appropriate evolution equation for their synchronization manifold, which can also be defined for different types of synchronization. The exact synchronization bound assures an exponential stabilization of the synchronization manifold which is crucial for applications. The analytical synchronization bound is independent of the nature of the modulation and can be applied to any time-delay system satisfying a Lipschitz condition. The analytical results are corroborated numerically using the Ikeda system
4-[3-(1H-Imidazol-1-yl)propyl]-3-methyl-5-(thiophen-2-ylmethyl)-4H-1,2,4-triazole monohydrate
In the title compound, C14H17N5S·H2O, the triazole ring makes dihedral angles of 48.15 (8) and 84.92 (8)° with the imidazole and thiophenyl rings, respectively. The water molecule is involved in intermolecular O—H⋯N hydrogen bonding
Dynamics of FitzHugh-Nagumo excitable systems with delayed coupling
Small lattices of nearest neighbor coupled excitable FitzHugh-Nagumo
systems, with time-delayed coupling are studied, and compared with systems of
FitzHugh-Nagumo oscillators with the same delayed coupling. Bifurcations of
equilibria in N=2 case are studied analytically, and it is then numerically
confirmed that the same bifurcations are relevant for the dynamics in the case
. Bifurcations found include inverse and direct Hopf and fold limit cycle
bifurcations. Typical dynamics for different small time-lags and coupling
intensities could be excitable with a single globally stable equilibrium,
asymptotic oscillatory with symmetric limit cycle, bi-stable with stable
equilibrium and a symmetric limit cycle, and again coherent oscillatory but
non-symmetric and phase-shifted. For an intermediate range of time-lags inverse
sub-critical Hopf and fold limit cycle bifurcations lead to the phenomenon of
oscillator death. The phenomenon does not occur in the case of FitzHugh-Nagumo
oscillators with the same type of coupling.Comment: accepted by Phys.Rev.
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