scholarly journals Van der Pol's oscillator under the parametric and forced excitations

2007 ◽  
Vol 29 (3) ◽  
pp. 207-219
Author(s):  
Nguyen Van Dao ◽  
Nguyen Van Dinh ◽  
Tran Kim Chi
Keyword(s):  
Small Parameter ◽  
Chaotic Behavior ◽  
Deterministic System ◽  
First Approximation ◽  
First Case ◽  
Oscillator Type ◽  
Resonance Curves ◽  
The Stability ◽  
The Given

Van der Pol's oscillator under parametric and forced excitations is studied. The case where the system contains a small parameter being quasilinear and the general case (without assumption on the smallness of nonlinear terms and perturbations) are studied. In the first case, equations of the first approximation are obtained by means of the Krylov-Bogoliubov-Mitropolskii technique, their averaging is performed, frequency amplitude and resonance curves are studied, on the stability of the given system is considered. In the second case, the possibility of chaotic behavior in a deterministic system of oscillator type is shown.

scholarly journals Dynamic Effects Arise Due to Consumers’ Preferences Depending on Past Choices

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 173 ◽  
Author(s):  
Sameh S. Askar ◽  
A. Al-khedhairi
Keyword(s):  
Numerical Simulation ◽  
Fixed Points ◽  
Chaotic Behavior ◽  
Logistic Map ◽  
Dynamic Effects ◽  
One Dimensional ◽  
First Case ◽  
The Stability ◽  
Conditions Of Stability ◽  
Dynamic Duopoly

We analyzed a dynamic duopoly game where players adopt specific preferences. These preferences are derived from Cobb–Douglas utility function with the assumption that they depend on past choices. For this paper, we investigated two possible cases for the suggested game. The first case considers only focusing on the action done by one player. This action reduces the game’s map to a one-dimensional map, which is the logistic map. Using analytical and numerical simulation, the stability of fixed points of this map is studied. In the second case, we focus on the actions applied by both players. The fixed points, in this case, are calculated, and their stability is discussed. The conditions of stability are provided in terms of the game’s parameters. Numerical simulation is carried out to give local and global investigations of the chaotic behavior of the game’s map. In addition, we use a statistical measure, such as entropy, to get more evidences on the regularity and predictability of time series associated with this case.

A fixed point approach to the stability of sextic Lie *-derivations

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4933-4944
Author(s):  
Dongseung Kang ◽  
Heejeong Koh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Single Case ◽  
Fixed Point Method ◽  
Point Method ◽  
Fixed Point Approach ◽  
The Stability ◽  
The Given ◽  
Lie Derivations

We obtain a general solution of the sextic functional equation f (ax+by)+ f (ax-by)+ f (bx+ay)+ f (bx-ay) = (ab)2(a2 + b2)[f(x+y)+f(x-y)] + 2(a2-b2)(a4-b4)[f(x)+f(y)] and investigate the stability of sextic Lie *-derivations associated with the given functional equation via fixed point method. Also, we present a counterexample for a single case.

Applications of random graphs

2017 ◽  
Author(s):  
A.C.C. Coolen ◽  
A. Annibale ◽  
E.S. Roberts
Keyword(s):  
Social Networks ◽  
Random Graphs ◽  
Interaction Network ◽  
Power Grids ◽  
Protein Protein Interaction ◽  
Topological Features ◽  
First Case ◽  
The Stability ◽  
Protein Protein Interaction Network

This chapter reviews graph generation techniques in the context of applications. The first case study is power grids, where proposed strategies to prevent blackouts have been tested on tailored random graphs. The second case study is in social networks. Applications of random graphs to social networks are extremely wide ranging – the particular aspect looked at here is modelling the spread of disease on a social network – and how a particular construction based on projecting from a bipartite graph successfully captures some of the clustering observed in real social networks. The third case study is on null models of food webs, discussing the specific constraints relevant to this application, and the topological features which may contribute to the stability of an ecosystem. The final case study is taken from molecular biology, discussing the importance of unbiased graph sampling when considering if motifs are over-represented in a protein–protein interaction network.

The Tangled Tale of Phase Space

2018 ◽  
Author(s):  
David D. Nolte
Keyword(s):  
Phase Space ◽  
Chaotic Behavior ◽  
Three Body Problem ◽  
Henri Poincaré ◽  
History Of ◽  
The Stability ◽  
Three Body ◽  
Space Phase ◽  
Central Paradigm ◽  
System Phase

This chapter presents the history of the development of the concept of phase space. Phase space is the central visualization tool used today to study complex systems. The chapter describes the origins of phase space with the work of Joseph Liouville and Carl Jacobi that was later refined by Ludwig Boltzmann and Rudolf Clausius in their attempts to define and explain the subtle concept of entropy. The turning point in the history of phase space was when Henri Poincaré used phase space to solve the three-body problem, uncovering chaotic behavior in his quest to answer questions on the stability of the solar system. Phase space was established as the central paradigm of statistical mechanics by JW Gibbs and Paul Ehrenfest.

scholarly journals The two-dimensional hydrodynamical theory of moving aerofoils. IV

1947 ◽  
Vol 188 (1015) ◽  
pp. 439-463
Keyword(s):  
Stability Problem ◽  
Two Dimensional ◽  
Centre Of Gravity ◽  
First Approximation ◽  
Von Karman ◽  
Moving Cylinder ◽  
Period Equation ◽  
The Stability ◽  
Von Kármán ◽  
Hydrodynamical Theory

In the first part of this paper opportunity has been taken to make some adjustments in certain general formulae of previous papers, the necessity for which appeared in discussions with other workers on this subject. The general results thus amended are then applied to a general discussion of the stability problem including the effect of the trailing wake which was deliberately excluded in the previous paper. The general conclusion is that to a first approximation the wake, as usually assumed, has little or no effect on the reality of the roots of the period equation, but that it may introduce instability of the oscillations, if the centre of gravity of the element is not sufficiently far forward. During the discussion contact is made with certain partial results recently obtained by von Karman and Sears, which are shown to be particular cases of the general formulae. An Appendix is also added containing certain results on the motion of a vortex behind a moving cylinder, which were obtained to justify certain of the assumptions underlying the trail theory.

scholarly journals Explicit parallel co-simulation approach: analysis and improved coupling method based on H-infinity synthesis

2021 ◽  
Author(s):  
Weitao Chen ◽  
Shenhai Ran ◽  
Canhui Wu ◽  
Bengt Jacobson
Keyword(s):  
Frequency Domain ◽  
Wide Frequency Range ◽  
Coupling Method ◽  
Sampled Data ◽  
H Infinity ◽  
First Case ◽  
Communication Step ◽  
Coupling Variables ◽  
The Stability ◽  
Stability And Accuracy

AbstractCo-simulation is widely used in the industry for the simulation of multidomain systems. Because the coupling variables cannot be communicated continuously, the co-simulation results can be unstable and inaccurate, especially when an explicit parallel approach is applied. To address this issue, new coupling methods to improve the stability and accuracy have been developed in recent years. However, the assessment of their performance is sometimes not straightforward or is even impossible owing to the case-dependent effect. The selection of the coupling method and its tuning cannot be performed before running the co-simulation, especially with a time-varying system.In this work, the co-simulation system is analyzed in the frequency domain as a sampled-data interconnection. Then a new coupling method based on the H-infinity synthesis is developed. The method intends to reconstruct the coupling variable by adding a compensator and smoother at the interface and to minimize the error from the sample-hold process. A convergence analysis in the frequency domain shows that the coupling error can be reduced in a wide frequency range, which implies good robustness. The new method is verified using two co-simulation cases. The first case is a dual mass–spring–damper system with random parameters and the second case is a co-simulation of a multibody dynamic (MBD) vehicle model and an electric power-assisted steering (EPAS) system model. Experimental results show that the method can improve the stability and accuracy, which enables a larger communication step to speed up the explicit parallel co-simulation.

Pressure dependent ultrasonic properties of hcp hafnium metal

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ramanshu P. Singh ◽  
Shakti Yadav ◽  
Giridhar Mishra ◽  
Devraj Singh
Keyword(s):  
Elastic Constants ◽  
Pressure Range ◽  
Room Temperature ◽  
Ultrasonic Attenuation ◽  
Coupling Constants ◽  
Ultrasonic Properties ◽  
Acoustic Coupling ◽  
Third Order Elastic Constants ◽  
The Stability ◽  
The Given

Abstract The elastic and ultrasonic properties have been evaluated at room temperature between the pressure 0.6 and 10.4 GPa for hexagonal closed packed (hcp) hafnium (Hf) metal. The Lennard-Jones potential model has been used to compute the second and third order elastic constants for Hf. The elastic constants have been utilized to calculate the mechanical constants such as Young’s modulus, bulk modulus, shear modulus, Poisson’s ratio, and Zener anisotropy factor for finding the stability and durability of hcp hafnium metal within the chosen pressure range. The second order elastic constants were also used to compute the ultrasonic velocities along unique axis at different angles for the given pressure range. Further thermophysical properties such as specific heat per unit volume and energy density have been estimated at different pressures. Additionally, ultrasonic Grüneisen parameters and acoustic coupling constants have been found out at room temperature. Finally, the ultrasonic attenuation due to phonon–phonon interaction and thermoelastic mechanisms has been investigated for the chosen hafnium metal. The obtained results have been discussed in correlation with available findings for similar types of hcp metals.

scholarly journals Some remarks on the stability of the Cauchy equation and completeness

2021 ◽  
Author(s):  
Harald Fripertinger ◽  
Jens Schwaiger
Keyword(s):  
Normed Space ◽  
Additive Function ◽  
Functional Equations ◽  
Constant Function ◽  
Cauchy Equation ◽  
Cauchy Difference ◽  
International Conference ◽  
The Difference ◽  
The Stability ◽  
The Given

AbstractIt was proved in Forti and Schwaiger (C R Math Acad Sci Soc R Can 11(6):215–220, 1989), Schwaiger (Aequ Math 35:120–121, 1988) and with different methods in Schwaiger (Developments in functional equations and related topics. Selected papers based on the presentations at the 16th international conference on functional equations and inequalities, ICFEI, Bȩdlewo, Poland, May 17–23, 2015, Springer, Cham, pp 275–295, 2017) that under the assumption that every function defined on suitable abelian semigroups with values in a normed space such that the norm of its Cauchy difference is bounded by a constant (function) is close to some additive function, i.e., the norm of the difference between the given function and that additive function is also bounded by a constant, the normed space must necessarily be complete. By Schwaiger (Ann Math Sil 34:151–163, 2020) this is also true in the non-archimedean case. Here we discuss the situation when the bound is a suitable non-constant function.

Chaos Control for a Fractional-Order Jerk System via Time Delay Feedback Controller and Mixed Controller

2021 ◽  
Vol 5 (4) ◽  
pp. 257
Author(s):  
Changjin Xu ◽  
Maoxin Liao ◽  
Peiluan Li ◽  
Lingyun Yao ◽  
Qiwen Qin ◽  
...  
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Chaos Control ◽  
Chaotic Behavior ◽  
Control Strategies ◽  
Feedback Controller ◽  
Research Approach ◽  
Controlling Chaos ◽  
The Stability ◽  
Jerk System

In this study, we propose a novel fractional-order Jerk system. Experiments show that, under some suitable parameters, the fractional-order Jerk system displays a chaotic phenomenon. In order to suppress the chaotic behavior of the fractional-order Jerk system, we design two control strategies. Firstly, we design an appropriate time delay feedback controller to suppress the chaos of the fractional-order Jerk system. The delay-independent stability and bifurcation conditions are established. Secondly, we design a suitable mixed controller, which includes a time delay feedback controller and a fractional-order PDσ controller, to eliminate the chaos of the fractional-order Jerk system. The sufficient condition ensuring the stability and the creation of Hopf bifurcation for the fractional-order controlled Jerk system is derived. Finally, computer simulations are executed to verify the feasibility of the designed controllers. The derived results of this study are absolutely new and possess potential application value in controlling chaos in physics. Moreover, the research approach also enriches the chaos control theory of fractional-order dynamical system.

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