scholarly journals A note on symmetry breaking in a non linear marketing model

2021 ◽  
Author(s):  
Andrea Caravaggio ◽  
Lorenzo Cerboni Baiardi ◽  
Mauro Sodini
Keyword(s):  
Symmetry Breaking ◽  
Numerical Simulations ◽  
Discrete Time ◽  
Original Model ◽  
Market Size ◽  
Multiple Attractors ◽  
Time Dynamic ◽  
Marketing Model ◽  
Adaptive Adjustment ◽  
Adjustment Mechanisms

AbstractIn this paper, we consider the nonlinear discrete-time dynamic model proposed by Bischi and Baiardi (Chaos Solitons Fractals 79:145-156, 2015a). The model considers players with adaptive adjustment mechanisms towards the best reply and a form of inertia in adopting such mechanism. Moreover, we formulate an extension of the original model, where endogenous market size is considered. Through numerical simulations, we show that multiple attractors may exist in the presence of homogeneous agents and the emergence of non-synchronized trajectories both in the short (on-off intermittency) and long (global riddling) run. Therefore, the article highlights that strategic contexts exist in which the players’ knowledge of the market and the adoption of the best reply do not always allow the use of the representative agent’s rhetoric to describe the dynamics of the model.

scholarly journals Search for a moving target in a competitive environment

2021 ◽  
Author(s):  
Benoit Duvocelle ◽  
János Flesch ◽  
Hui Min Shi ◽  
Dries Vermeulen
Keyword(s):  
Markov Chain ◽  
Discrete Time ◽  
Competitive Environment ◽  
Moving Target ◽  
Time Varying ◽  
Greedy Strategy ◽  
Time Dynamic ◽  
Dynamic Search ◽  
Subgame Perfect Equilibria ◽  
Perfect Equilibria

AbstractWe consider a discrete-time dynamic search game in which a number of players compete to find an invisible object that is moving according to a time-varying Markov chain. We examine the subgame perfect equilibria of these games. The main result of the paper is that the set of subgame perfect equilibria is exactly the set of greedy strategy profiles, i.e. those strategy profiles in which the players always choose an action that maximizes their probability of immediately finding the object. We discuss various variations and extensions of the model.

An algebraic study of Diodorean modal systems

1965 ◽  
Vol 30 (1) ◽  
pp. 58-64 ◽  
Author(s):  
R. A. Bull
Keyword(s):  
Discrete Time ◽  
Decision Procedure ◽  
John Locke ◽  
Original Model ◽  
Completeness Proof ◽  
Semantic Tableaux ◽  
Algebraic Treatment ◽  
Algebraic Result ◽  
Modal Systems

Attention was directed to modal systems in which ‘necessarily α’ is interpreted as ‘α. is and always will be the case’ by Prior in his John Locke Lectures of 1956. The present paper shows that S4.3, the extension of S4 withALCLpLqLCLqLp,is complete with respect to this interpretation when time is taken to be continuous, and that D, the extension of S4.3 withALNLpLCLCLCpLpLpLp,is complete with respect to this interpretation when time is taken to be discrete. The method employed depends upon the application of an algebraic result of Garrett Birkhoff's to the models for these systems, in the sense of Tarski.A considerable amount of work on S4.3 and D precedes this paper. The original model with discrete time is given in Prior's [7] (p. 23, but note the correction in [8]); that taking time to be continuous yields a weaker system is pointed out by him in [9]. S4.3 and D are studied in [3] of Dummett and Lemmon, where it is shown that D includes S4.3 andCLCLCpLpLpCMLpLp.While in Oxford in 1963, Kripke proved that these were in fact sufficient for D, using semantic tableaux. A decision procedure for S4.3, using Birkhoff's result, is given in my [2]. Dummett conjectured, in a conversation, that taking time to be continuous yielded S4.3. Thus the originality of this paper lies in giving a suitable completeness proof for S4.3, and in the unified algebraic treatment of the systems. It should be emphasised that the credit for first axiomatising D belongs to Kripke.

Amplitude Modulation and Symmetry Breaking Bifurcation in Micro Devices

2012 ◽  
Author(s):  
Z. C. Feng ◽  
Mahmoud Almasri
Keyword(s):  
Symmetry Breaking ◽  
Numerical Simulations ◽  
Amplitude Modulation ◽  
Dynamic Responses ◽  
Symmetric Structure ◽  
Different Types ◽  
Asymmetric Responses ◽  
Symmetric Response ◽  
Symmetry Breaking Bifurcation

Designs of many micro devices take advantage of the symmetry for better performance, immunity to noise, and for simpler analysis. When a symmetric structure is subjected to symmetric forcing, the symmetric response can become unstable leading to asymmetric responses. The occurrence of symmetry breaking bifurcation leads to complicated dynamic responses which often result in less desirable performances. In this paper, we obtain analytical criteria for the onset of symmetry breaking bifurcations. We also conduct numerical simulations to demonstrate different types of asymmetric dynamic responses resulting from the symmetry breaking bifurcation. In particular, we show the occurrence of amplitude modulated motions in such systems.

Discrete-Time Robust Control of Linear Periodically Time-Varying Systems

2007 ◽  
Author(s):  
S. Kalender ◽  
H. Flashner
Keyword(s):  
Robust Control ◽  
Discrete Time ◽  
Robustness Analysis ◽  
Value Theory ◽  
Time Varying ◽  
Sampled Data ◽  
Point Mapping ◽  
Time Dynamic ◽  
Time Representation ◽  
Time Varying Systems

An approach for robust control of periodically time-varying systems is proposed. The approach combines the point-mapping formulation and a parameterization of the control vector to formulate an equivalent time-invariant discrete-time representation of the system. The discrete-time representation of the dynamic system allows for the application of known sampled-data control design methodologies. A perturbed, discrete-time dynamic model is formulated and plant parametric uncertainty are obtained using a truncated point-mapping algorithm. The error bounds due to point-mapping approximation are computed and a robustness analysis problem of the system due to parametric uncertainties is formulated using structured singular value theory. The proposed approach is illustrated by two design examples. Simulation studies show good performance robustness of the control system to parameter perturbations and system nonlinearities.

scholarly journals Discrete-Time Dynamic Image-Segmentation System

10.5772/14281 ◽  
2011 ◽  
Author(s):  
Kenichi Fujimoto ◽  
Mio Kobayashi ◽  
Tetsuya Yoshinag
Keyword(s):  
Image Segmentation ◽  
Discrete Time ◽  
Time Dynamic ◽  
Dynamic Image
Sign in / Sign up

Export Citation Format

Share Document