On Solutions and Stability of Stochastic Functional Equations Emerging in Psychological Theory of Learning

Turab, Ali; Brzdęk, Janusz; Ali, Wajahat

doi:10.3390/axioms11030143

Cited by 4 publications

(1 citation statement)

References 27 publications

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“…Numerous further investigations on human (see [22][23][24][25][26][27]) and animal (see [28][29][30][31]) behavior within probability learning settings have generated diverse findings.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Class of Stochastic Animal Behavior Models under Specific Choice Preferences

et al. 2022

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The behavior of animals can be studied in two ways: experimentally, in labs or in the field, or theoretically, via modeling. Extensive research on animal behavior in probabilistic learning circumstances has produced findings that are consistent with so-called occurrence studies. However, such cases can be classified into four different events, depending on the location of the food and the side chosen by the animals. This article sought to overcome these limitations by offering a generic stochastic model under these conditions that can be utilized to analyze the broad range of models that have been reported in the literature. We explored the existence, uniqueness, and stability results of the proposed model using well-known fixed-point methods. Additionally, we present some examples to highlight the significance of our results.

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“…Numerous further investigations on human (see [22][23][24][25][26][27]) and animal (see [28][29][30][31]) behavior within probability learning settings have generated diverse findings.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Class of Stochastic Animal Behavior Models under Specific Choice Preferences

et al. 2022

Self Cite

View full text Add to dashboard Cite

show abstract

Computational modeling of animal behavior in T-mazes: Insights from machine learning

Turab,

Sintunavarat,

Ullah

et al. 2024

Ecological Informatics

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On a unique solution and stability analysis of a class of stochastic functional equations arising in learning theory

Turab

2022

Analysis

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Numerous computational and learning theory models have been studied using probabilistic functional equations. Especially in two-choice scenarios, the vast bulk of animal behavior research divides such situations into two different events. They split these actions into two possibilities according to the animals’ progress toward a particular decision. However, reward plays a crucial role in such experiments because, based on the selected side and the food placement, such scenarios may be classified into four distinct categories. This article aims to explore the animals’ reactions to such circumstances by presenting a generic stochastic functional equation. By using the well-known fixed point theory results, we examine the existence, uniqueness, and stability of solutions to the suggested functional equation. Moreover, an example is included to emphasize the significance of our findings.

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On Solutions and Stability of Stochastic Functional Equations Emerging in Psychological Theory of Learning

Cited by 4 publications

References 27 publications

Analysis of a Class of Stochastic Animal Behavior Models under Specific Choice Preferences

Analysis of a Class of Stochastic Animal Behavior Models under Specific Choice Preferences

Computational modeling of animal behavior in T-mazes: Insights from machine learning

On a unique solution and stability analysis of a class of stochastic functional equations arising in learning theory

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