Abstract: In this work we make a bifurcation analysis for a
single compartment representation of Traub model, one of the most
important conductance-based models. The analysis focus in two
principal parameters: current and leakage conductance. Study of
stable and unstable solutions are explored; also Hop-bifurcation and
frequency interpretation when current varies is examined. This study
allows having control of neuron dynamics and neuron response when
these parameters change. Analysis like this is particularly important
for several applications such as: tuning parameters in learning
process, neuron excitability tests, measure bursting properties of the
neuron, etc. Finally, a hardware implementation results were
developed to corroborate these results.
Abstract: This paper is devoted to the study of a viscous
incompressible flow around a circular cylinder performing harmonic
oscillations, especially the steady streaming phenomenon. The
research methodology is based on the asymptotic explanation method
combined with the computational bifurcation analysis. The research
approach develops Schlichting and Wang decomposition method.
Present studies allow to identify several regimes of the secondary
streaming with different flow structures. The results of the research
are in good agreement with experimental and numerical simulation
data.
Abstract: In this paper, a delayed plankton-nutrient interaction model consisting of phytoplankton, zooplankton and dissolved nutrient is considered. It is assumed that some species of phytoplankton releases toxin (known as toxin producing phytoplankton (TPP)) which is harmful for zooplankton growth and this toxin releasing process follows a discrete time variation. Using delay as bifurcation parameter, the stability of interior equilibrium point is investigated and it is shown that time delay can destabilize the otherwise stable non-zero equilibrium state by inducing Hopf-bifurcation when it crosses a certain threshold value. Explicit results are derived for stability and direction of the bifurcating periodic solution by using normal form theory and center manifold arguments. Finally, outcomes of the system are validated through numerical simulations.
Abstract: In this paper, we consider a two-neuron system with time-delayed connections between neurons. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulation results are given to support the theoretical predictions. Finally, main conclusions are given.
Abstract: In this paper, we consider a discrete Gompertz model with time delay. Firstly, the stability of the equilibrium of the system is investigated by analyzing the characteristic equation. By choosing the time delay as a bifurcation parameter, we prove that Neimark- Sacker bifurcations occur when the delay passes a sequence of critical values. The direction and stability of the Neimark-Sacker are determined by using normal forms and centre manifold theory. Finally, some numerical simulations are given to verify the theoretical analysis.
Abstract: In this paper, applying frequency domain approach, a delayed predator-prey fishery model with prey reserve is investigated. By choosing the delay τ as a bifurcation parameter, It is found that Hopf bifurcation occurs as the bifurcation parameter τ passes a sequence of critical values. That is, a family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value. The length of delay which preserves the stability of the positive equilibrium is calculated. Some numerical simulations are included to justify the theoretical analysis results. Finally, main conclusions are given.
Abstract: Horizontal platform system (HPS) is popularly applied
in offshore and earthquake technology, but it is difficult and
time-consuming for regulation. In order to understand the nonlinear
dynamic behavior of HPS and reduce the cost when using it, this paper
employs differential transformation method to study the bifurcation
behavior of HPS. The numerical results reveal a complex dynamic
behavior comprising periodic, sub-harmonic, and chaotic responses.
Furthermore, the results reveal the changes which take place in the
dynamic behavior of the HPS as the external torque is increased.
Therefore, the proposed method provides an effective means of
gaining insights into the nonlinear dynamics of horizontal platform
system.
Abstract: This study presents a systematic analysis of the
dynamic behaviors of a gear-bearing system with porous squeeze film
damper (PSFD) under nonlinear suspension, nonlinear oil-film force
and nonlinear gear meshing force effect. It can be found that the
system exhibits very rich forms of sub-harmonic and even the chaotic
vibrations. The bifurcation diagrams also reveal that greater values of
permeability may not only improve non-periodic motions effectively,
but also suppress dynamic amplitudes of the system. Therefore, porous
effect plays an important role to improve dynamic stability of
gear-bearing systems or other mechanical systems. The results
presented in this study provide some useful insights into the design
and development of a gear-bearing system for rotating machinery that
operates in highly rotational speed and highly nonlinear regimes.
Abstract: In this paper, a delayed physiological control system is investigated. The sufficient conditions for stability of positive equilibrium and existence of local Hopf bifurcation are derived. Furthermore, global existence of periodic solutions is established by using the global Hopf bifurcation theory. Finally, numerical examples are given to support the theoretical analysis.
Abstract: The dynamics of a delayed mathematical model for
Hes1 oscillatory expression are investigated. The linear stability of
positive equilibrium and existence of local Hopf bifurcation are
studied. Moreover, the global existence of large periodic solutions
has been established due to the global bifurcation theorem.
Abstract: A stage-structured predator-prey system with two time delays is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated and the existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results. Based on the global Hopf bifurcation theorem for general functional differential equations, the global existence of periodic solutions is established.
Abstract: In this paper, stability and Hopf bifurcation analysis of
a novel hyperchaotic system are investigated. Four feedback control
strategies, the linear feedback control method, enhancing feedback
control method, speed feedback control method and delayed feedback
control method, are used to control the hyperchaotic attractor to
unstable equilibrium. Moreover numerical simulations are given to
verify the theoretical results.
Abstract: In this paper, a delayed predator–prey system with stage
structure is investigated. Sufficient conditions for the system to have
multiple periodic solutions are obtained when the delay is sufficiently
large by applying Bendixson-s criterion. Further, some numerical
examples are given.