Motivation and information in motor performance: modelling of self-efficacy and knowledge of results interaction in a timing task

BACKGROUND: Despite the literature positing a strong relation between motor performance and self-efficacy, few studies address the phenomenon formally. In this sense, how self-efficacy modulates corrections in a trial-to-trial basis and how the performance that individuals consider to be satisfactory modulate both corrections and self-efficacy are not well understood. AIM: The aim of this study is to develop and evaluate a model that relates self-efficacy and performance through a system of difference equations. METHOD: First, we demonstrate the model’s capabilities through constrained simulations. The, to evaluate the model’s grasp of empirical data, we parameterized the model to capture the constant, variable error, self-efficacy and believed satisfactory performance for each individual. RESULTS: The model demonstrates capacity to reproduce these summary results when initial conditions are fed to the system of difference equations. However, we observe features that must be improved and qualitative deviations when individuals demonstrate highly variable behavior. CONCLUSION: The initial results support the current assumptions and included variables in this model.

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On the Solutions of the System of Difference Equationsxn+1=max{A/xn,yn/xn},yn+1=max{A/yn,xn/yn}

Discrete Dynamics in Nature and Society ◽

10.1155/2009/325296 ◽

2009 ◽

Vol 2009 ◽

pp. 1-11 ◽

Cited By ~ 3

Author(s):

Dağistan Simsek ◽

Bilal Demir ◽

Cengiz Cinar

Keyword(s):

Difference Equations ◽

Initial Conditions ◽

Real Numbers ◽

System Of Difference Equations ◽

Positive Real

We study the behavior of the solutions of the following system of difference equationsxn+1=max⁡{A/xn,yn/xn},yn+1=max⁡{A/yn,xn/yn}where the constantAand the initial conditions are positive real numbers.

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Long-term behavior of positive solutions of an exponentially self-regulating system of difference equations

International Journal of Biomathematics ◽

10.1142/s1793524517500450 ◽

2017 ◽

Vol 10 (03) ◽

pp. 1750045 ◽

Cited By ~ 1

Author(s):

N. Psarros ◽

G. Papaschinopoulos ◽

K. B. Papadopoulos

Keyword(s):

Asymptotic Behavior ◽

Positive Solutions ◽

Difference Equations ◽

Initial Conditions ◽

System Of Difference Equations ◽

Long Term Behavior

In this paper, we study the asymptotic behavior of the positive solutions of a system of the following difference equations: [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] are positive constants and the initial conditions [Formula: see text] and [Formula: see text] are positive numbers.

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Dynamics of a Higher-Order System of Difference Equations

Discrete Dynamics in Nature and Society ◽

10.1155/2017/4312640 ◽

2017 ◽

Vol 2017 ◽

pp. 1-9

Author(s):

Qi Wang ◽

Qinqin Zhang ◽

Qirui Li

Keyword(s):

Positive Integer ◽

Positive Solutions ◽

Difference Equations ◽

Initial Conditions ◽

Higher Order ◽

Order System ◽

Real Numbers ◽

Precise Description ◽

System Of Difference Equations ◽

Positive Real

Consider the following system of difference equations:xn+1(i)=xn-m+1(i)/Ai∏j=0m-1xn-j(i+j+1)+αi,xn+1(i+m)=xn+1(i),x1-l(i+l)=ai,l,Ai+m=Ai,αi+m=αi,i,l=1,2,…,m;n=0,1,2,…,wheremis a positive integer,Ai,αi,i=1,2,…,m, and the initial conditionsai,l,i,l=1,2,…,m,are positive real numbers. We obtain the expressions of the positive solutions of the system and then give a precise description of the convergence of the positive solutions. Finally, we give some numerical results.

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Eventually Periodic Solutions of a Max-Type System of Difference Equations of Higher Order

Discrete Dynamics in Nature and Society ◽

10.1155/2018/8467682 ◽

2018 ◽

Vol 2018 ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

Guangwang Su ◽

Taixiang Sun ◽

Bin Qin

Keyword(s):

Periodic Solutions ◽

Difference Equations ◽

Initial Conditions ◽

Type System ◽

Higher Order ◽

System Of Difference Equations

We study in this paper the following max-type system of difference equations of higher order: xn=max{A,yn-k/xn-1} and yn=max{B,xn-k/yn-1}, n∈{0,1,2,…}, where A≥B>0, k≥1, and the initial conditions x-k,y-k,x-k+1,y-k+1,…,x-1,y-1∈(0,+∞). We show that (1) if AB>1, then every solution of the above system is periodic with period 2 eventually. (2) If AB=1>B, then every solution of the above system is periodic with period 2k or 2 eventually. (3) If A=B=1 or AB<1, then the above system has a solution which is not periodic eventually.

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Codynamics of Four Variables Involved in Dengue Transmission and Its Control by Community Intervention: A System of Four Difference Equations

Discrete Dynamics in Nature and Society ◽

10.1155/2014/101965 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8

Author(s):

T. Awerbuch-Friedlander ◽

Richard Levins ◽

M. Predescu

Keyword(s):

Difference Equations ◽

Community Intervention ◽

Initial Conditions ◽

System Of Difference Equations ◽

Open Problems ◽

Infected People ◽

Dengue Transmission ◽

Nature And Society ◽

And Control

In the case of Dengue transmission and control, the interaction of nature and society is captured by a system of difference equations. For the purpose of studying the dynamics of these interactions, four variables involved in a Dengue epidemic, proportion of infected people (P), number of mosquitoes involved in transmission (M), mosquito habitats (H), and population awareness (A), are linked in a system of difference equations:Pn+1=aPn+1-e-iMn1-Pn,Mn+1=lMne-An+bHn1-e-Mn,Hn+1=cHn/(1+pAn)+1/(1+qAn), andAn+1=rAn+fPn,n=0,1,…. The constraints have socioecological meaning. The initial conditions are such that0≤P0≤1, (M0,H0,A0)≥(0,0,0), the parametersl,a,c,r∈(0,1), and the parametersf, i, b, andpare positive. The paper is concerned with the analysis of solutions of the above system forp=q. We studied the global asymptotic stability of the degenerate equilibrium. We also propose extensions of the above model and some open problems. We explored the role of memory in community awareness by numerical simulations. When the memory parameter is large, the proportion of infected people decreases and stabilizes at zero. Below a critical point we observe periodic oscillations.

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On the Solutions of a General System of Difference Equations

Discrete Dynamics in Nature and Society ◽

10.1155/2012/892571 ◽

2012 ◽

Vol 2012 ◽

pp. 1-12 ◽

Cited By ~ 11

Author(s):

E. M. Elsayed ◽

M. M. El-Dessoky ◽

Abdullah Alotaibi

Keyword(s):

Difference Equations ◽

Initial Conditions ◽

General System ◽

Real Numbers ◽

System Of Difference Equations ◽

The Difference

We deal with the solutions of the systems of the difference equationsxn+1=1/xn-pyn-p,yn+1=xn-pyn-p/xn-qyn-q, andxn+1=1/xn-pyn-pzn-p,yn+1=xn-pyn-pzn-p/xn-qyn-qzn-q,zn+1=xn-qyn-qzn-q/xn-ryn-rzn-r, with a nonzero real numbers initial conditions. Also, the periodicity of the general system ofkvariables will be considered.

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Solution of the Maximum of Difference Equation xn+1=max{Axn−1,ynxn};yn+1=max{Ayn−1,xnyn}\matrix{ {x_{n + 1} = max \left\{ {{A \over {x_{n - 1} }},{{y_n } \over {x_n }}} \right\};} & {y_{n + 1} = max \left\{ {{A \over {y_{n - 1} }},{{x_n } \over {y_n }}} \right\}}}

Applied Mathematics and Nonlinear Sciences ◽

10.2478/amns.2020.1.00025 ◽

2020 ◽

Vol 5 (1) ◽

pp. 275-282

Author(s):

Dagistan Simsek ◽

Burak Ogul ◽

Fahreddin Abdullayev

Keyword(s):

Difference Equation ◽

Difference Equations ◽

Initial Conditions ◽

Type System ◽

Global Behavior ◽

System Of Difference Equations

AbstractIn the recent years, there has been a lot of interest in studying the global behavior of, the socalled, max-type difference equations; see, for example, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]. The study of max type difference equations has also attracted some attention recently. We study the behaviour of the solutions of the following system of difference equation with the max operator: paper deals with the behaviour of the solutions of the max type system of difference equations, (1)\matrix{ {x_{n + 1} = max \left\{ {{A \over {x_{n - 1} }},{{y_n } \over {x_n }}} \right\};} & {y_{n + 1} = max \left\{ {{A \over {y_{n - 1} }},{{x_n } \over {y_n }}} \right\},}} where the parametr A and initial conditions x−1,x0, y−1,y0 are positive reel numbers.

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