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Title Design of Morlet Wavelet Artificial Neural Network for solving Two-Species Competition Model

Author(s) Nimra Noor

Abstract Artificial Neural Networks (ANNs) have gained significant interest in solving mathematical and biological problems due to their powerful learning and approximation capabilities. The study of Two-Species Competition Model using nonlinear differential equations is a crucial area of computational mathematics and biomathematics. This thesis introduces a novel computational approach using ANN and a hybrid optimization framework to study the dynamics of species interactions. This thesis developed a hybrid optimization method using Sequential Quadratic Programming (SQP) and Genetic Algorithm (GA) to precisely approximate the solution of the Two-Species Competition Model. This model captures competitive behavior between two biological species over time using a feedforward ANN architecture with a Morlet wavelet (MW) activation function for enhanced learning capacity. The ANN-GA-SQP method is designed to efficiently and accurately solve complex ecological systems, demonstrating its potential as a powerful tool for modeling and understanding complex ecosystems. To verify the robustness, accuracy, and consistency of the proposed ANN-based approach 50 experimental runs were conducted for each test scenario of the Two-Species Competition Model. The hybrid GA-SQP optimized ANN model outperforms conventional numerical methods and hybrid optimization techniques in terms of convergence dependability, numerical stability, and predictive accuracy, as evaluated using statistical measures like Mean Absolute Deviation (MAD) and Mean Square Error MSE analysis. Overall the study demonstrates the effectiveness of neuroevolutionary methods in solving nonlinear differential equations in ecological modeling. The GA-SQP optimized ANN framework, incorporating Morlet wavelet activation function, offers a reliable, adaptable, and biologically inspired computational tool for complex dynamical systems.

Type Thesis/Dissertation MS

Faculty Engineering and Computer Science

Department Mathematics

Language English

Publication Date 2025-11-25

Subject Mathematics

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