Abstract: This paper deals with bifurcation analyses in current programmed DC/DC Boost converter and exhibition of chaotic behavior. This phenomenon occurs due to variation of a set of the studied circuit parameters (input voltage and a reference current). Two different types of bifurcation paths have been observed as part as part of another bifurcation arising from variation of suitable chosen parameter.
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: The objective in this work is to generate and discuss the stability results of fully-immersed end-milling process with parameters; tool mass m=0.0431kg,tool natural frequency ωn = 5700 rads^-1, damping factor ξ=0.002 and workpiece cutting coefficient C=3.5x10^7 Nm^-7/4. Different no of teeth is considered for the end-milling. Both 1-DOF and 2-DOF chatter models of the system are generated on the basis of non-linear force law. Chatter stability analysis is carried out using a modified form (generalized for both 1-DOF and 2-DOF models) of recently developed method called Full-discretization. The full-immersion three tooth end-milling together with higher toothed end-milling processes has secondary Hopf bifurcation lobes (SHBL’s) that exhibit one turning (minimum) point each. Each of such SHBL is demarcated by its minimum point into two portions; (i) the Lower Spindle Speed Portion (LSSP) in which bifurcations occur in the right half portion of the unit circle centred at the origin of the complex plane and (ii) the Higher Spindle Speed Portion (HSSP) in which bifurcations occur in the left half portion of the unit circle. Comments are made regarding why bifurcation lobes should generally get bigger and more visible with increase in spindle speed and why flip bifurcation lobes (FBL’s) could be invisible in the low-speed stability chart but visible in the high-speed stability chart of the fully-immersed three-tooth miller.
Abstract: The characteristics of physiological blood flow in human carotid arterial bifurcation model have been numerically studied using a fully coupled fluid-structure interaction (FSI) analysis. This computational model with the fluid-structure interaction is constructed to investigate the flow characteristics and wall shear stress in the carotid artery. As the flow begins to decelerate after the peak flow, a large recirculation zone develops at the non-divider wall of both internal carotid artery (ICA) and external carotid artery (ECA) in FSI model due to the elastic energy stored in the expanding compliant wall. The calculated difference in wall shear stress (WSS) in both Non-FSI and FSI models is a range of between 5 and 11% at the mean WSS. The low WSS corresponds to regions of carotid artery that are more susceptible to atherosclerosis.
Abstract: An Ivlev-type predator-prey system and stage-structured for predator concerning impulsive control strategy is considered. The conditions for the locally asymptotically stable prey-eradication periodic solution is obtained, by using Floquet theorem and small amplitude perturbation skills——when the impulsive period is less than the critical value. Otherwise, the system is permanence. Numerical examples show that the system considered has more complicated dynamics, including high-order quasi-periodic and periodic oscillating, period-doubling and period-halving bifurcation, chaos and attractor crisis, etc. Finally, the biological implications of the results and the impulsive control strategy are discussed.
Abstract: In this paper, a FitzHugh-Nagumo model with time delays is investigated. The linear stability of the equilibrium and the existence of Hopf bifurcation with delay τ is investigated. By applying Nyquist criterion, the length of delay is estimated for which stability continues to hold. Numerical simulations for justifying the theoretical results are illustrated. Finally, main conclusions are given.
Abstract: In this paper, a delayed Nicholson,s blowflies model with a linear harvesting term is investigated. Regarding the delay as a bifurcation parameter, we show that Hopf bifurcation will occur when the delay crosses a critical value. Numerical simulations supporting the theoretical findings are carried out.
Abstract: A mathematical model is proposed considering the forest biomass density B(t), density of wood based industries W(t) and density of synthetic industries S(t). It is assumed that the forest biomass grows logistically in the absence of wood based industries, but depletion of forestry biomass is due to presence of wood based industries. The growth of wood based industries depends on B(t), while S(t) grows at a constant rate, independent of B(t). Further there is a competition between W(t) and S(t) according to market demand. The proposed model has four ecologically feasible steady states, namely, E1: forest biomass free and wood industries free equilibrium; E2: wood industries free equilibrium and two coexisting equilibria E∗1 , E∗2 . Behavior of the system near all feasible equilibria is analyzed using the stability theory of differential equations. In the proposed model, the natural depletion rate h1 is a crucial parameter and system exhibits Hopf-bifurcation about the non-trivial equilibrium with respect to h1. The analytical results are verified using numerical simulation.
Abstract: This paper studies the effect of time delay on stability
of mutualism population model with limited resources for both
species. First, the stability of the model without time delay is
analyzed. The model is then improved by considering a time delay in
the mechanism of the growth rate of the population. We analyze the
effect of time delay on the stability of the stable equilibrium point.
Result showed that the time delay can induce instability of the stable
equilibrium point, bifurcation and stability switches.
Abstract: In this paper, different nonlinear dynamics analysis techniques are employed to unveil the rich nonlinear phenomena of the electromagnetic system. In particular, bifurcation diagrams, time responses, phase portraits, Poincare maps, power spectrum analysis, and the construction of basins of attraction are all powerful and effective tools for nonlinear dynamics problems. We also employ the method of Lyapunov exponents to show the occurrence of chaotic motion and to verify those numerical simulation results. Finally, two cases of a chaotic electromagnetic system being effectively controlled by a reference signal or being synchronized to another nonlinear electromagnetic system are presented.
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: A dynamic of Bertrand duopoly game is analyzed, where players use different production methods and choose their prices with bounded rationality. The equilibriums of the corresponding discrete dynamical systems are investigated. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability of Nash equilibrium, as some parameters of the model are varied, gives rise to complex dynamics such as cycles of higher order and chaos. On this basis, we discover that an increase of adjustment speed of bounded rational player can make Bertrand market sink into the chaotic state. Finally, the complex dynamics, bifurcations and chaos are displayed by numerical simulation.
Abstract: DC-DC converters are widely used in regulated switched mode power supplies and in DC motor drive applications. There are several sources of unwanted nonlinearity in practical power converters. In addition, their operation is characterized by switching that gives birth to a variety of nonlinear dynamics. DC-DC buck and boost converters controlled by pulse-width modulation (PWM) have been simulated. The voltage waveforms and attractors obtained from the circuit simulation have been studied. With the onset of instability, the phenomenon of subharmonic oscillations, quasi-periodicity, bifurcations, and chaos have been observed. This paper is mainly motivated by potential contributions of chaos theory in the design, analysis and control of power converters, in particular and power electronics circuits, in general.
Abstract: A theoretical approach to radiation damage evolution
is developed. Stable temporal behavior taking place in solids under
irradiation are examined as phenomena of self-organization in nonequilibrium
systems.
Experimental effects of temporal self-organization in solids under
irradiation are reviewed. Their essential common properties and
features are highlighted and analyzed.
Dynamical model to describe development of self-oscillation of
density of point defects under stationary irradiation is proposed. The
emphasis is the nonlinear couplings between rate of annealing and
density of defects that determine the kind and parameters of an
arising self-oscillation.
The field of parameters (defect generation rate and environment
temperature) at which self-oscillations develop is found. Bifurcation
curve and self-oscillation period near it is obtained.
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: Nonlinear response behaviour of a cracked RC beam under harmonic excitation is analysed to investigate various instability phenomena like, bifurcation, jump phenomena etc. The nonlinearity of the system arises due to opening and closing of the cracks in the RC beam and is modelled as a cubic polynomial. In order to trace different branches at the bifurcation point on the response curve (amplitude versus frequency of excitation plot), an arc length continuation technique along with the incremental harmonic balance (IHBC) method is employed. The stability of the solution is investigated by the Floquet theory using Hsu-s scheme. The periodic solutions obtained by the IHBC method are compared with these obtained by the numerical integration of the equation of motion. Characteristics of solutions fold bifurcation, jump phenomena and from stable to unstable zones are identified.
Abstract: By utilizing the system of the recurrence equations, containing two parameters, the dynamics of two antagonistically interconnected populations is studied. The following areas of the system behavior are detected: the area of the stable solutions, the area of cyclic solutions occurrence, the area of the accidental change of trajectories of solutions, and the area of chaos and fractal phenomena. The new two-dimensional diagram of the dynamics of the solutions change (the fractal cabbage) has been obtained. In the cross-section of this diagram for one of the equations the well-known Feigenbaum tree of doubling has been noted.Keywordsbifurcation, chaos, dynamics of populations, fractals
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: Mathematical models can be used to describe the
dynamics of the spread of infectious disease between susceptibles
and infectious populations. Dengue fever is a re-emerging disease in
the tropical and subtropical regions of the world. Its incidence has
increased fourfold since 1970 and outbreaks are now reported quite
frequently from many parts of the world. In dengue endemic regions,
more cases of dengue infection in pregnancy and infancy are being
found due to the increasing incidence. It has been reported that
dengue infection was vertically transmitted to the infants. Primary
dengue infection is associated with mild to high fever, headache,
muscle pain and skin rash. Immune response includes IgM antibodies
produced by the 5th day of symptoms and persist for 30-60 days. IgG
antibodies appear on the 14th day and persist for life. Secondary
infections often result in high fever and in many cases with
hemorrhagic events and circulatory failure. In the present paper, a
mathematical model is proposed to simulate the succession of dengue
disease transmission in pregnancy and infancy. Stability analysis of
the equilibrium points is carried out and a simulation is given for the
different sets of parameter. Moreover, the bifurcation diagrams of our
model are discussed. The controlling of this disease in infant cases is
introduced in the term of the threshold condition.