Dynamic Stability Analysis of Size-Dependent Viscoelastic/Piezoelectric Nano-beam

This paper analyzes the dynamic stability of an isotropic viscoelastic Euler–Bernoulli nano-beam using piezoelectric materials. For this purpose, the size-dependent theory was used in the framework of the modified couple stress theory (MCST) for piezoelectric materials. In order to capture the geometrical nonlinearity, the von Karman strain displacement relation was applied. Hamilton’s principle was also employed to obtain the governing equations. Furthermore, the Galerkin method was used in order to convert the governing partial differential equations (PDEs) to a nonlinear second-order ordinary differential one. Dynamic stability analysis was performed and the effects of such parameters as viscoelastic coefficients, size effect, and piezoelectric coefficient were investigated. The results showed that in this system, saddle points, central points, Hopf bifurcation points, and fork bifurcation points could be created, and the phase portraits connecting these equilibrium points exhibit periodic orbits, heteroclinic orbits, and homoclinic orbits.

Dynamics and bifurcations of a ratio-dependent predator-prey model

In this paper, we study a ratio-dependent predator-prey model with modied Holling-Tanner formalism, by using dynamical techniques and numerical continuation algorithms implemented in Matcont. We determine codim-1 and 2 bifurcation points and their corresponding normal form coecients. We also compute a curve of limit cycles of the system emanating from a Hopf point.

Periodic, Quasi-Periodic and Phase-Locked Oscillations and Stability in the Fiscal Dynamical Model with Tax Collection and Decision-Making Delays

In this paper, we consider the complex dynamics of a fiscal dynamical model, which was improved from Wolfstetter classical growth cycle model by Sportelli et al. The main work of the present paper is to study the impact of fiscal policy delays on the national income adjustment processes using a dynamical method, such as double Hopf bifurcation analysis. We first use DDE-BIFTOOL to find the double Hopf bifurcation points of the system, and draw the bifurcation diagrams with two bifurcation parameters, i.e. the tax collection delay [Formula: see text] and the public expenditure decision-making delay [Formula: see text]. Then we employ the method of multiple scales to obtain two amplitude equations. By analyzing these amplitude equations, we derive the classification and unfolding of these double Hopf bifurcation points. And three types of double Hopf bifurcations are found. Finally, we verify the results by numerical simulations. We find complex dynamic behaviors of the system via the analytical method, such as stable equilibrium, stable periodic, quasi-periodic and phase-locked solutions in respective regions. The dynamical phenomena can help policy makers to choose a proper range of the delays so that they could effectively formulate fiscal policies to stabilize the economy.

Phase Transitions and Bifurcation Points in the Initiation Dynamics of Venture Emergence: A Conceptual Framework

Based on isomorphic considerations, this paper attempts to establish an entrepreneur as complex adaptive system, which is one of the concepts that appear prominently in the field of complexity sciences. The attempt to equate the notion of an entrepreneur with the idea of a complex adaptive system, presupposes recognition of the entrepreneur’s role in adaptive agency. Along with this recognition, comes the convenience of contextualizing the concepts of phase transitions and bifurcation points in terms of venture emergence. The dynamics of these concepts are however more commonly explored within the workings of complex or dynamic physical systems. Yet, the broad applicability of the underlying ideas offers the possibility of identifying similar concepts in biological systems and by extension, the field of entrepreneurial cognition and behavior. Thus, the paper adopts an interdisciplinary approach and employs retroductive reasoning in the assemblage of relevant ideas, sought from diverse literary sources. The outcome is a conceptual framework, which presents certain propositions that offer implication for action.

Geometrically nonlinear analysis of the stability of the stiffened plate taking into account the interaction of eigenforms of buckling

The aims of this work are a detailed consideration in a geometrically nonlinear formulation of the stages of the equilibrium behavior of a compressed stiffened plate, taking into account the interaction of the general form of buckling and local forms of wave formation in the plate or in the reinforcing ribs, comparison of the results of the semi-analytical solution of the system of nonlinear equations with the results of the numerical solution on the Patran-Nastran FEM complex of the problem of subcritical and postcritical equilibrium of a compressed stiffened plate. Methods. Geometrically-nonlinear analysis of displacement fields, deformations and stresses, calculation of eigenforms of buckling and construction of bifurcation solutions and solutions for equilibrium curves with limit points depending on the initial imperfections. An original method is proposed for determining critical states and obtaining bilateral estimates of critical loads at limiting points. Results. An algorithm for studying the equilibrium states of a stiffened plate near critical points is described in detail and illustrated by examples, using the first nonlinear (cubic terms) terms of the potential energy expansion, the coordinates of bifurcation points and limit points, as well as the corresponding values of critical loads. The curves of the critical load sensitivity are plotted depending on the value of the initial imperfections of the total deflection. Equilibrium curves with characteristic bifurcation points of local wave formation are constructed using a numerical solution. For the case of action of two initial imperfections, an algorithm is proposed for obtaining two-sided estimates of critical loads at limiting points.

THE LIAR’S PARADOX –A WILD INTERATION. PART II. DIFTHONG «ARISTOTEL-ANOKHIN» (CONTINUATION)

There are more and more precedents with offended infants of 30-40 years old — they are not emotionally abstinent, because they are in an artificial coma of infantilism, in which ‘desire’ has replaced ‘sacrifice’, and are clearly hypocritical, which is why the Holiday of Disobedience, hanging around the planet with a blinking garland of conflicts and wars, creates a turbulent zone in which the bifurcation points are taken out — beyond the orbit of common understanding, turning Consciousness into the quietest Sphinx, producing hypotheses. The saying, willingly or unwittingly, can become a “winged missile” — and destroy the whole world, good or bad, but the theory created by the presentiment of scientific research can help keep it in health and in the flesh of a divine plan, but on one condition: while maintaining peace and the will of Consciousness — the indispensable parity of the Mind, which multiplies both entities and doubt as paradox, whose mental albatrosses format our understanding. Thus, a hypothesis based on a paradox forms the Image of the Concept, and thereby builds a fundamental frame of the worldview, without belittling the elephants, and without forgetting the whale. In our world, a liar as Caesar’s wife turns out to be beyond suspicion, and, therefore, discussion, and his figure is so transparent and nano-technological that it has long been soldered into the ‘scale of errors’ of all perception — and this is the toothless sperm whale that substituted its back for the pillars of thinking, which is why not only looms as a wise turtle, but is also perceived by a cheerful Buddha. From time to time, the whale opens its mouth — and we all find ourselves in its throat, and the liar himself is outside the Law, outside the conflict, but in the Law: in the legal field of the Absolute, who knows only the doctrine of exclusiveness and the purple of shamelessness is accustomed.

Nonlinear Vibration and Stability Analysis of Functionally Graded Nanobeam Subjected to External Parametric Excitation and Thermal Load

Analysis of vibration stability of simply supported Euler-Bernoulli functionally graded (FG) nanobeam embedded in viscous elastic medium with thermal effect under external parametric excitation is presented in this work. An attempt has been made for the first time is investigating the effect of thermal load on dynamic behavior, amplitude response, instability region and bifurcation points of functionally graded nanobeam. Thermal loads are supposed to be uniform, linear or nonlinear distribution along the thickness direction. Nonlocal continuum theory and the principle of the minimum total potential energy are applied to derive the governing equations. The partial differential equations (PDE) are transported to the ordinary differential equations (ODE) by using the Petrov-Galerkin method and the multiple time scales method are manipulated to solve the motion equation. To study the effect of external parametric excitation and thermal effect, different temperature distributions along the thickness such as uniform, linear, and nonlinear distribution are considered. Moreover, stable and unstable regions and bifurcation points are determined. It is obtained that the thermal load can affect the amplitude response of FG nanobeam. Also, it is observed that the instability of the system is affected by the detuning parameter and the parametric excitation amplitude plays great role in the instability of system. Nanobeams are used in many devices like nanoresonators, nanosensors and nanoswitches. This paper is helpful for designing and manufacturing nanoscale structures specially nanoresonators under different thermal loads.

Territorial communities consolidation route

The paper addresses the problem on the consolidation of local communities, by which authors refer to the purposefully organized and regulated process of strengthening interpersonal and intergroup ties in a community. By consolidation route, the authors understand the process of mass consciousness modification of the territorial community, consisting in the successive (step-by-step) approval of the prerequisites for the assimilation of the consolidation idea as a behavioural norm. At each stage, however, bifurcation points and risks of not achieving the planned results are likely to emerge. Regulation in this case involves the application of point effects in bifurcation situations, the creation of conditions for movement in the desired direction, and the motivation of various groups of the territorial community to pass the route.

Predicting Tipping Points in Chaotic Maps with Period-Doubling Bifurcations

In this paper, bifurcation points of two chaotic maps are studied: symmetric sine map and Gaussian map. Investigating the properties of these maps shows that they have a variety of dynamical solutions by changing the bifurcation parameter. Sine map has symmetry with respect to the origin, which causes multistability in its dynamics. The systems’ bifurcation diagrams show various dynamics and bifurcation points. Predicting bifurcation points of dynamical systems is vital. Any bifurcation can cause a huge wanted/unwanted change in the states of a system. Thus, their predictions are essential in order to be prepared for the changes. Here, the systems’ bifurcations are studied using three indicators of critical slowing down: modified autocorrelation method, modified variance method, and Lyapunov exponent. The results present the efficiency of these indicators in predicting bifurcation points.