Analysis of a Class of Stochastic Animal Behavior Models under Specific Choice Preferences
Abstract
:1. Introduction and Preliminaries
- We propose a general functional equation with more than two options, focusing on food location and the chosen side;
- Our proposed model generalizes many models in the existing literature and opens a new avenue of research within mathematical psychology and learning theory;
- We also discuss Hyers–Ulam and Hyers–Ulam–Rassias stability for the proposed system;
- We present some examples to show the importance of our results within this field of study.
2. Main Results
- Let be a class containing all continuous real-value functions satisfying and where and with . There is also a subset of , such that is a Banach space (for details, see [17]);
- Let be contraction mappings with contractive coefficients , respectively, with ;
- Let be a non-expansive mapping with for and ;
- The mappings satisfy the following conditions:
- Let be a fixed function. Then, for every that satisfies , there is a unique , such that and for ;
- Let . Then, for every that satisfies , there is a unique , such that and for .
- Let be contraction mappings with contractive coefficients , respectively, with .
- Points exist such that and .
3. Stability Analysis
4. Some Illustrative Examples
5. Conclusions
- Is there another method for establishing the conclusions of Theorems 2 and 3?
- Is it possible to prove Theorem 2 without using Condition ?
- What would happen if an animal did not react to any particular trial?
- Can we extend the proposed approach to discuss the behavior of animals in situations with more than four choices?
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Placement of Food | Side Chosen by Rat | Probability of Occurrence |
---|---|---|
A: Left Side | Left Turn (Food Side) | |
A: Left Side | Right Turn (Non-Food Side) | |
B: Right Side | Right Turn (Food Side) | |
B: Right Side | Left Turn (Non-Food Side) |
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Turab, A.; Mlaiki, N.; Fatima, N.; Mitrović, Z.D.; Ali, W. Analysis of a Class of Stochastic Animal Behavior Models under Specific Choice Preferences. Mathematics 2022, 10, 1975. https://doi.org/10.3390/math10121975
Turab A, Mlaiki N, Fatima N, Mitrović ZD, Ali W. Analysis of a Class of Stochastic Animal Behavior Models under Specific Choice Preferences. Mathematics. 2022; 10(12):1975. https://doi.org/10.3390/math10121975
Chicago/Turabian StyleTurab, Ali, Nabil Mlaiki, Nahid Fatima, Zoran D. Mitrović, and Wajahat Ali. 2022. "Analysis of a Class of Stochastic Animal Behavior Models under Specific Choice Preferences" Mathematics 10, no. 12: 1975. https://doi.org/10.3390/math10121975
APA StyleTurab, A., Mlaiki, N., Fatima, N., Mitrović, Z. D., & Ali, W. (2022). Analysis of a Class of Stochastic Animal Behavior Models under Specific Choice Preferences. Mathematics, 10(12), 1975. https://doi.org/10.3390/math10121975