Mathematical modeling in cognitive science and neural systems
D. Sathis Kumardean_sp@adityauniversity.inSchool of PharmacyAditya UniversitySurampalem, Andhra Pradesh, 533437, IndiaView full profile → , *Rameshwar D. ChintamaniCorresponding authorchintamanirameshwarit@sanjivani.org.inDepartment of Information TechnologySanjivani College of EngineeringSavitribai Phule Pune UniversityKopargaon, Ahilyanagar, Maharashtra, 423603, IndiaView full profile → , Dheeraj Kalradheeraj.kalra@gla.ac.inDepartment of Electronics & Communications EngineeringGLA UniversityMathura, Uttar Pradesh, 281406, IndiaView full profile → , Satyadharma Bhartis.bharti@rungta.orgDepartment of Computer Science and EngineeringRungta College of Engineering and TechnologyRungta International Skills UniversityBhilai, Chhattisgarh, 490024, IndiaView full profile → , Pallavi M. Tekadepmtekade_it@jspmrscoe.edu.inDepartment of Information TechnologyJSPM’s Rajarshi Shahu College of EngineeringPune, Maharashtra, 411033, IndiaView full profile → , Romya Singhdrromyasingh3@gmail.comDepartment of MicrobiologyNoida International UniversityGreater Noida, Uttar Pradesh, 201312, IndiaView full profile → , Shwetambari Pandurang Katakeshwetambari.katake@vit.eduDepartment of Computer EngineeringVishwakarma Institute of TechnologyPune, Maharashtra, 411037, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Apr 2026
- Published Online:
- 27 Oct 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2829
- Pages:
- 3183–3194
Abstract
A growing need in the field of cognitive science is to develop mathematical tools that relate the functioning of the brain to perception, memory, learning and decision making. In this study, an integrated dynamical model consisting of coupled nonlinear differential equations, neural activation functions, synaptic plasticity and external stimuli, representing cognitive states is proposed. The framework provides a set of biologically interpretable parameters for excitation, inhibition, connectivity, decay, adaptation and noise and stability and equilibrium analyses describe long term behavior. The numerical simulations provide an assessment of activity propagation, state transitions, convergence and sensitivity with different parameter sets. Results show that balanced excitation and inhibition lead to a stable cognitive representation while stronger coupling and/or noise lead to oscillatory and unstable responses. The computational power of the model provides a framework for understanding the neural mechanisms, comparing cognitive scenarios and informing the development of brain-inspired intelligent systems and clinically relevant investigations of cognition and behavior.
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References
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