• Computers and Concrete
• /
• 제3권4호
• /
• pp.213-233
• /
• 2006

Over the past years techniques for non-linear analysis have been enhanced significantly via improved solution procedures, extended finite element techniques and increased robustness of constitutive models. Nevertheless, problems remain, especially for real world structures of softening materials like concrete. The softening gives negative stiffness and risk of bifurcations due to multiple cracks that compete to survive. Incremental-iterative techniques have difficulties in selecting and handling the local peaks and snap-backs. In this contribution, an alternative method is proposed. The softening diagram of negative slope is replaced by a saw-tooth diagram of positive slopes. The incremental-iterative Newton method is replaced by a series of linear analyses using a special scaling technique with subsequent stiffness/strength reduction per critical element. It is shown that this event-by-event strategy is robust and reliable. First, the model is shown to be objective with respect to mesh refinement. Next, the example of a large-scale dog-bone specimen in direct tension is analyzed using an isotropic version of the saw-tooth model. The model is capable of automatically providing the snap-back response. Subsequently, the saw-tooth model is extended to include anisotropy for fixed crack directions to accommodate both tensile cracking and compression strut action for reinforced concrete. Three different reinforced concrete structures are analyzed, a tension-pull specimen, a slender beam and a slab. In all cases, the model naturally provides the local peaks and snap-backs associated with the subsequent development of primary cracks starting from the rebar. The secant saw-tooth stiffness is always positive and the analysis always 'converges'. Bifurcations are prevented due to the scaling technique.

• Advances in nano research
• /
• 제10권4호
• /
• pp.359-371
• /
• 2021

A tumor immune interaction is a main topic of interest in the last couple of decades because majority of human population suffered by tumor, formed by the abnormal growth of cells and is continuously interacted with the immune system. Because of its wide range of applications, many researchers have modeled this tumor immune interaction in the form of ordinary, delay and fractional order differential equations as the majority of biological models have a long range temporal memory. So in the present work, tumor immune interaction in fractional form provides an excellent tool for the description of memory and hereditary properties of inter and intra cells. So the interaction between effector-cells, tumor cells and interleukin-2 (IL-2) are modeled by using the definition of Caputo fractional order derivative that provides the system with long-time memory and gives extra degree of freedom. Moreover, in order to achieve more efficient computational results of fractional-order system, a discretization process is performed to obtain its discrete counterpart. Furthermore, existence and local stability of fixed points are investigated for discrete model. Moreover, it is proved that two types of bifurcations such as Neimark-Sacker and flip bifurcations are studied. Finally, numerical examples are presented to support our analytical results.

• Kyungpook Mathematical Journal
• /
• 제60권2호
• /
• pp.335-347
• /
• 2020

In this paper, we take into account a parasite-host system with reaction-diffusion. Firstly, we derive conditions for Hopf, Turing, and wave bifurcations of the system in the spatial domain by means of linear stability and bifurcation analysis. Secondly, we display numerical simulations in order to investigate Turing pattern formation. In fact, the numerical simulation discloses that typical Turing patterns, such as spotted, spot-stripelike mixtures and stripelike patterns, can be formed. In this study, we show that typical Turing patterns, which are well known in predator-prey systems ([7, 18, 25]), can be observed in a parasite-host system as well.

• 대한기계학회논문집B
• /
• 제30권7호
• /
• pp.630-637
• /
• 2006

The flow regimes for a Taylor-Couette flow with a stable, axial stratification in density are investigated using numerical simulation. The flow configuration identical to that in the experiment of Boubnov, et al. (1995) is considered in the present research. The main objectives of this investigation are to verify the experimental and numerical results carried out by Boubnov, et al. and Hua et al. (1997), respectively, and to further study the detailed flow fields and flow bifurcations. With increasing buoyancy frequency of the fluid (N), the stratification-dominated flow regime, called the S-regime, is observed. It is also confirmed that the important effect of an axial density stratification is to stabilize the flow field. The present numerical results are in good agreement with Boubnov, et al. and Hua et al.'s observations.

• Journal of applied mathematics & informatics
• /
• 제29권5_6호
• /
• pp.1193-1204
• /
• 2011

In the present paper we consider a differential-algebraic prey-predator model with stage structure for prey and harvesting of predator species. Stability and instability of the equilibrium points are discussed and it is observed that the model exhibits a singular induced bifurcation when the economic profit is zero. It indicates that the zero economic profit brings impulse, i.e. rapid expansion of the population and the system collapses. For the purpose of stabilizing the system around the positive equilibrium, a state feedback controller is designed. Finally, numerical simulations are given to show the consistency with theoretical analysis.

• 대한수학회보
• /
• 제50권2호
• /
• pp.353-373
• /
• 2013

In this paper, a class of delayed predator-prey models of prey migration and predator switching is considered. 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 simulations for justifying the theoretical analysis are also provided. Finally, biological explanations and main conclusions are given.

• Journal of Power Electronics
• /
• 제14권6호
• /
• pp.1208-1216
• /
• 2014

Mismatch between switching frequency and circuit parameters often occurs in industrial applications, which would lead to instability phenomena. The bifurcation behavior of $V^2$ controlled buck converter is investigated as the pulse width modulation period is varied. Nonlinear behavior is analyzed based on the monodromy matrix of the system. We observed that the stable period-1 orbit was first transformed to the period-2 bifurcation, which subsequently changed to chaos. The mechanism of the series of period-2 bifurcations shows that the characteristic eigenvalue of the monodromy matrix passes through the unit circle along the negative real axis. Resonant parametric perturbation technique has been applied to prevent the onset of instability. Meanwhile, the extended stability region of the converter is obtained. Simulation and experimental prototypes are built, and the corresponding results verify the theoretical analysis.

• KIEE International Transactions on Power Engineering
• /
• 제4A권1호
• /
• pp.1-5
• /
• 2004

The model of a power system with load dynamics is studied by investigating qualitative changes in its behavior as the reactive power demand at a load bus is increased. The load is created using induction motors parallel with the constant power and constant impedance load. As the load increases, the system experiences various bifurcations such as sub critical and supercritical Hopf, period-doubling and saddle-node bifurcation. The latter may lead the system to voltage collapse. A nonlinear controller is used to control the subcritical Hopf bifurcation and hence mitigate voltage collapse. It is applied to the KEPCO (Korean Electric Power Company) system to demonstrate its validity.

• Journal of Mechanical Science and Technology
• /
• 제17권12호
• /
• pp.1994-2003
• /
• 2003

The vibration of a flexible cantilever tube with nonlinear constraints when it is subjected to flow internally with fluids is examined by experimental and theoretical analysis. These kinds of studies have been performed to find the existence of chaotic motion. In this paper, the important parameters of the system leading to such a chaotic motion such as Young's modulus and the coefficient of viscoelastic damping are discussed. The parameters are investigated by means of system identification so that comparisons are made between numerical analysis using the design parameters and the experimental results. The chaotic region led by several period-doubling bifurcations beyond the Hopf bifurcation is also re-established with phase portraits, bifurcation diagram and Lyapunov exponent so that one can define optimal parameters for system design.

• Smart Structures and Systems
• /
• 제4권4호
• /
• pp.407-428
• /
• 2008

The nonlinear mechanics of cable vibration is caught either by analytical or numerical models. Nevertheless, the choice of the most appropriate method, in consideration of the problem under study, is not straightforward. A feedback control policy might even enhance the complexity of the system. Thus, in order to design a suitable controller, different approaches are here adopted. Devices mounted transversely to the cable in the two directions, close to one of its ends, supply the feedback control action based on the observation of the response in a few points. The low order terms of the control law are, at first, analyzed in the framework of linear models. Explicit analytic solutions are derived for this purpose. The effectiveness of high order terms in the control law is then explored by means of a finite element model(FEM), which accounts for high order harmonics. A suitably dimensional analytical Galerkin model is finally derived, to investigate the effectiveness of the proposed control strategy, when applied to a physical model.