Abstract: In this paper, for the understanding of the phytoplankton dynamics in marine ecosystem, a susceptible and an infected class of phytoplankton population is considered in spatiotemporal domain.
Here, the susceptible phytoplankton is growing logistically and the
growth of infected phytoplankton is due to the instantaneous Holling
type-II infection response function. The dynamics are studied in terms of the local and global stabilities for the system and further
explore the possibility of Hopf -bifurcation, taking the half saturation period as (i.e., ) the bifurcation parameter in temporal domain.
It is also observe that the reaction diffusion system exhibits spatiotemporal
chaos and pattern formation in phytoplankton dynamics,
which is particularly important role play for the spatially extended phytoplankton system. Also the effect of the diffusion coefficient
on the spatial system for both one and two dimensional case is obtained. Furthermore, we explore the higher-order stability analysis
of the spatial phytoplankton system for both linear and no-linear system. Finally, few numerical simulations are carried out for pattern
formation.
Abstract: The effect of a time delay on the transmission on
dengue fever is studied. The time delay is due to the presence of an
incubation period for the dengue virus to develop in the mosquito
before the mosquito becomes infectious. The conditions for the
existence of a Hopf bifurcation to limit cycle behavior are
established. The conditions are different from the usual one and they
are based on whether a particular third degree polynomial has
positive real roots. A theorem for determining whether for a given
set of parameter values, a critical delay time exist is given. It is
found that for a set of realistic values of the parameters in the model,
a Hopf bifurcation can not occur. For a set of unrealistic values of
some of the parameters, it is shown that a Hopf bifurcation can occur.
Numerical solutions using this last set show the trajectory of two of
the variables making a transition from a spiraling orbit to a limit
cycle orbit.
Abstract: The dynamics of a predator-prey model with continuous
threshold policy harvesting functions on the prey is studied. Theoretical
and numerical methods are used to investigate boundedness
of solutions, existence of bionomic equilibria, and the stability properties
of coexistence equilibrium points and periodic orbits. Several
bifurcations as well as some heteroclinic orbits are computed.
Abstract: We study bifurcation structure of the zonal jet flow the
streamfunction of which is expressed by a single spherical harmonics
on a rotating sphere. In the non-rotating case, we find that a steady
traveling wave solution arises from the zonal jet flow through Hopf
bifurcation. As the Reynolds number increases, several traveling
solutions arise only through the pitchfork bifurcations and at high
Reynolds number the bifurcating solutions become Hopf unstable. In
the rotating case, on the other hand, under the stabilizing effect of
rotation, as the absolute value of rotation rate increases, the number
of the bifurcating solutions arising from the zonal jet flow decreases
monotonically. We also carry out time integration to study unsteady
solutions at high Reynolds number and find that in the non-rotating
case the unsteady solutions are chaotic, while not in the rotating cases
calculated. This result reflects the general tendency that the rotation
stabilizes nonlinear solutions of Navier-Stokes equations.
Abstract: In this paper, a predator-prey model with time delay and habitat complexity is investigated. By analyzing the characteristic equations, the local stability of each feasible equilibria of the system is discussed and the existence of a Hopf bifurcation at the coexistence equilibrium is established. By choosing the sum of two delays as a bifurcation parameter, we show that Hopf bifurcations can occur as crosses some critical values. By deriving the equation describing the flow on the center manifold, we can determine the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main theoretical results.
Abstract: Endovascular aneurysm repair is a new and minimally invasive repair for patients with abdominal aortic aneurysm (AAA). This method has potential advantages that are incomparable with other repair methods. However, the enlargement of aneurysm in the absence of endoleak, which is known as endotension, may occur as one of post-operative compliances of this method. Typically, endotension is mainly as a result of pressure transmitted to aneurysm sac by endovascular installed graft. After installation of graft the aneurysm sac reduces significantly but remains non-zero. There are some factors which affect this pressure transmitted. In this study, the geometry features of installed vascular graft have been considered. It is inferred that graft neck angle and iliac bifurcation angle are two factors which can affect the drag force on graft and consequently the pressure transmitted to aneurysm.
Abstract: Semilinear elliptic equations are ubiquitous in natural sciences. They give rise to a variety of important phenomena in quantum mechanics, nonlinear optics, astrophysics, etc because they have rich multiple solutions. But the nontrivial solutions of semilinear equations are hard to be solved for the lack of stabilities, such as Lane-Emden equation, Henon equation and Chandrasekhar equation. In this paper, bifurcation method is applied to solving semilinear elliptic equations which are with homogeneous Dirichlet boundary conditions in 2D. Using this method, nontrivial numerical solutions will be computed and visualized in many different domains (such as square, disk, annulus, dumbbell, etc).
Abstract: In this paper, a three dimensional autonomous chaotic system is considered. The existence of Hopf bifurcation is investigated by choosing the appropriate bifurcation parameter. Furthermore, formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived with the help of normal form theory. Finally, a numerical example is given.
Abstract: In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated.With the help of computer algebra system MATHEMATICA, the first 10 quasi Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there exist 10 small amplitude limit cycles created from the three order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems. At last, we give an system which could bifurcate 10 limit circles.
Abstract: The present microfluidic study is emphasizing the flow behavior within a Y shape micro-bifurcation in two similar flow configurations. We report here a numerical and experimental investigation on the velocity profiles evolution and secondary flows, manifested at different Reynolds numbers (Re) and for two different boundary conditions. The experiments are performed using special designed setup based on optical microscopic devices. With this setup, direct visualizations and quantitative measurements of the path-lines are obtained. A Micro-PIV measurement system is used to obtain velocity profiles distributions in a spatial evolution in the main flows domains. The experimental data is compared with numerical simulations performed with commercial computational code FLUENT in a 3D geometry with the same dimensions as the experimental one. The numerical flow patterns are found to be in good agreement with the experimental manifestations.
Abstract: Within the collaborative research center 666 a new
product development approach and the innovative manufacturing
method of linear flow splitting are being developed. So far the design process is supported by 3D-CAD models utilizing User Defined
Features in standard CAD-Systems. This paper now presents new
functions for generating 3D-models of integral sheet metal products with bifurcations using Siemens PLM NX 6. The emphasis is placed
on design and semi-automated insertion of User Defined Features.
Therefore User Defined Features for both, linear flow splitting
and its derivative linear bend splitting, were developed. In order to facilitate the modeling process, an application was developed
that guides through the insertion process. Its usability and dialog layout adapt known standard features. The work presented here has
significant implications on the quality, accurateness and efficiency of the product generation process of sheet metal products with higher
order bifurcations.
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: The dynamics of User Datagram Protocol (UDP) traffic
over Ethernet between two computers are analyzed using nonlinear
dynamics which shows that there are two clear regimes in the data
flow: free flow and saturated. The two most important variables
affecting this are the packet size and packet flow rate. However,
this transition is due to a transcritical bifurcation rather than phase
transition in models such as in vehicle traffic or theorized large-scale
computer network congestion. It is hoped this model will help lay
the groundwork for further research on the dynamics of networks,
especially computer networks.
Abstract: A numerical study is presented on buckling and post
buckling behaviour of laminated carbon fiber reinforced plastic
(CFRP) thin-walled cylindrical shells under axial compression using
asymmetric meshing technique (AMT). Asymmetric meshing
technique is a perturbation technique to introduce disturbance without
changing geometry, boundary conditions or loading conditions.
Asymmetric meshing affects predicted buckling load, buckling mode
shape and post-buckling behaviour. Linear (eigenvalue) and nonlinear
(Riks) analyses have been performed to study the effect of
asymmetric meshing in the form of a patch on buckling behaviour.
The reduction in the buckling load using Asymmetric meshing
technique was observed to be about 15%. An isolated dimple formed
near the bifurcation point and the size of which increased to reach a
stable state in the post-buckling region. The load-displacement curve
behaviour applying asymmetric meshing is quite similar to the curve
obtained using initial geometric imperfection in the shell model.
Abstract: Chua’s circuit is one of the most important electronic devices that are used for Chaos and Bifurcation studies. A central role of secure communication is devoted to it. Since the adaptive control is used vastly in the linear systems control, here we introduce a new trend of application of adaptive method in the chaos controlling field. In this paper, we try to derive a new adaptive control scheme for Chua’s circuit controlling because control of chaos is often very important in practical operations. The novelty of this approach is for sake of its robustness against the external perturbations which is simulated as an additive noise in all measured states and can be generalized to other chaotic systems. Our approach is based on Lyapunov analysis and the adaptation law is considered for the feedback gain. Because of this, we have named it NAFT (Nonlinear Adaptive Feedback Technique). At last, simulations show the capability of the presented technique for Chua’s circuit.
Abstract: The structural stability of the model of a nonelectroneutral current sheath is investigated. The stationary model of a current sheath represents the system of four connected nonlinear differential first-order equations and thus they should manifest structural instability property, i.e. sensitivity to the infinitesimal changes of parameters and starting conditions. Domains of existence of the solutions of current sheath type are found. Those solutions of the current sheath type are realized only in some regions of sevendimensional space of parameters of the problem. The phase volume of those regions is small in comparison with the whole phase volume of the definition range of those parameters. It is shown that the offered model of a nonelectroneutral current sheath is applicable for theoretical interpretation of the bifurcational current sheaths observed in the magnetosphere.
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: Irradiated material is a typical example of a complex
system with nonlinear coupling between its elements. During
irradiation the radiation damage is developed and this development
has bifurcations and qualitatively different kinds of behavior.
The accumulation of primary defects in irradiated crystals is
considered in frame work of nonlinear evolution of complex system.
The thermo-concentration nonlinear feedback is carried out as a
mechanism of self-oscillation development.
It is shown that there are two ways of the defect density evolution
under stationary irradiation. The first is the accumulation of defects;
defect density monotonically grows and tends to its stationary state
for some system parameters. Another way that takes place for
opportune parameters is the development of self-oscillations of the
defect density.
The stationary state, its stability and type are found. The
bifurcation values of parameters (environment temperature, defect
generation rate, etc.) are obtained. The frequency of the selfoscillation
and the conditions of their development is found and
rated. It is shown that defect density, heat fluxes and temperature
during self-oscillations can reach much higher values than the
expected steady-state values. It can lead to a change of typical
operation and an accident, e.g. for nuclear equipment.