A Deterministic Model for Analyzing the Dynamics of Ant System Algorithm and Performance Amelioration through a New Pheromone Deposition Approach

Ant Colony Optimization (ACO) is a metaheuristic for solving difficult discrete optimization problems. This paper presents a deterministic model based on differential equation to analyze the dynamics of basic Ant System algorithm. Traditionally, the deposition of pheromone on different parts of the tour of a particular ant is always kept unvarying. Thus the pheromone concentration remains uniform throughout the entire path of an ant. This article introduces an exponentially increasing pheromone deposition approach by artificial ants to improve the performance of basic Ant System algorithm. The idea here is to introduce an additional attracting force to guide the ants towards destination more easily by constructing an artificial potential field identified by increasing pheromone concentration towards the goal. Apart from carrying out analysis of Ant System dynamics with both traditional and the newly proposed deposition rules, the paper presents an exhaustive set of experiments performed to find out suitable parameter ranges for best performance of Ant System with the proposed deposition approach. Simulations reveal that the proposed deposition rule outperforms the traditional one by a large extent both in terms of solution quality and algorithm convergence. Thus, the contributions of the article can be presented as follows: i) it introduces differential equation and explores a novel method of analyzing the dynamics of ant system algorithms, ii) it initiates an exponentially increasing pheromone deposition approach by artificial ants to improve the performance of algorithm in terms of solution quality and convergence time, iii) exhaustive experimentation performed facilitates the discovery of an algebraic relationship between the parameter set of the algorithm and feature of the problem environment.Comment: 4th IEEE International Conference on Information and Automation for Sustainability, 200

A Novel Parser Design Algorithm Based on Artificial Ants

This article presents a unique design for a parser using the Ant Colony Optimization algorithm. The paper implements the intuitive thought process of human mind through the activities of artificial ants. The scheme presented here uses a bottom-up approach and the parsing program can directly use ambiguous or redundant grammars. We allocate a node corresponding to each production rule present in the given grammar. Each node is connected to all other nodes (representing other production rules), thereby establishing a completely connected graph susceptible to the movement of artificial ants. Each ant tries to modify this sentential form by the production rule present in the node and upgrades its position until the sentential form reduces to the start symbol S. Successful ants deposit pheromone on the links that they have traversed through. Eventually, the optimum path is discovered by the links carrying maximum amount of pheromone concentration. The design is simple, versatile, robust and effective and obviates the calculation of the above mentioned sets and precedence relation tables. Further advantages of our scheme lie in i) ascertaining whether a given string belongs to the language represented by the grammar, and ii) finding out the shortest possible path from the given string to the start symbol S in case multiple routes exist.Comment: 4th IEEE International Conference on Information and Automation for Sustainability, 200

A Study of the Grunwald-Letnikov Definition for Minimizing the Effects of Random Noise on Fractional Order Differential Equations

Of the many definitions for fractional order differintegral, the Grunwald-Letnikov definition is arguably the most important one. The necessity of this definition for the description and analysis of fractional order systems cannot be overstated. Unfortunately, the Fractional Order Differential Equation (FODE) describing such a systems, in its original form, highly sensitive to the effects of random noise components inevitable in a natural environment. Thus direct application of the definition in a real-life problem can yield erroneous results. In this article, we perform an in-depth mathematical analysis the Grunwald-Letnikov definition in depth and, as far as we know, we are the first to do so. Based on our analysis, we present a transformation scheme which will allow us to accurately analyze generalized fractional order systems in presence of significant quantities of random errors. Finally, by a simple experiment, we demonstrate the high degree of robustness to noise offered by the said transformation and thus validate our scheme.Comment: 4th IEEE International Conference on Information and Automation for Sustainability, 200

Symmetric oscillator: Special features, realization, and combination synchronization

Researchers have recently paid significant attention to special chaotic systems. In this work, we introduce an oscillator with different special features. In addition, the oscillator is symmetrical. The features and oscillator dynamics are discovered through different tools of nonlinear dynamics. An electronic circuit is designed to mimic the oscillator’s dynamics. Moreover, the combined synchronization of two drives and one response oscillator is reported. Numerical examples illustrate the correction of our approach.This work is partially funded by Centre for Nonlinear Systems, Chennai Institute of Technology, India vide funding number CIT/CNS/2021/RD/064

The linearity of the master stability function

The master stability function (MSF) is a tool to evaluate the local stability of the synchronization in coupled oscillators. Computing the MSF of a network of a specific oscillator results in a curve whose shape is dependent on the nodes' dynamics, network topology, coupling function, and coupling strength. This paper calculates the MSF of networks of two diffusively coupled oscillators by considering different single variable and multi-variable couplings. Then, the linearity of the MSF is investigated by fitting a straight line to the MSF curve, and the root mean square error is obtained. It is observed that the multi-variable coupling with equal coefficients on all variables results in a linear MSF regardless of the dynamics of the nodes

Chaos in a memristive oscillator with six lines of equilibria

A novel memristive oscillator with infinite equilibria is proposed in this paper. The oscillator has six lines of equilibria, which make it different from known ones. Interestingly, the oscillator displays chaos and attractive features. Implementation of the oscillator via analog components is presented to verify its feasibility

A simple one-dimensional map-based model of spiking neurons with wide ranges of firing rates and complexities

This paper introduces a simple 1-dimensional map-based model of spiking neurons. During the past decades, dynamical models of neurons have been used to investigate the biology of human nervous systems. The models simulate experimental records of neurons’ voltages using difference or differential equations. Difference neuronal models have some advantages besides the differential ones. They are usually simpler, and considering the cost of needed computations, they are more efficient. In this paper, a simple 1-dimensional map-based model of spiking neurons is introduced. Sample entropy is applied to analyze the complexity of the model’s dynamics. The model can generate a wide range of time series with different firing rates and different levels of complexities. Besides, using some tools like bifurcation diagrams and cobwebs, the introduced model is analyzed