Non-linear Dynamics Commons^™

Digital Transformation And Market Microstructure: Analyzing The Impact Of Algorithmic Trading On National Stock Exchange Of India Price Discovery Mechanisms Through Complex Systems Theory., Mukesh Bhaskar Ahirrao, Harshal Anil Salunkhe, Vishal Sunil Rana

Northeast Journal of Complex Systems (NEJCS)

Abstract

This research examines the evolution of market microstructure at the National Stock Exchange of India (NSE) from 2020 to 2024, a period characterized by substantial growth in algorithmic trading from 35% to 44% of total trading volume. Using market microstructure data and analytical techniques grounded in complex systems perspectives, the study documents temporal patterns in price discovery, liquidity, volatility, and market efficiency associated with this digital transformation.

The analysis reveals several notable changes in market characteristics. Transaction costs improved significantly, with bid-ask spreads declining by 23.4% and market depth increasing by 18.1%. Price adjustment half-life decreased by 50%, indicating …

Complex Systems Mapping Of Fiscal Growth Dynamics At Strategic Maritime Chokepoints Using Time-Series Slopes, Rahul Balamurugan, Preethi Nanjundan, Avichal Sharma

Northeast Journal of Complex Systems (NEJCS)

This study examines how maritime and trading states allocate public resources between defence, health, and economic growth around three strategic chokepoints the Strait of Malacca, the Strait of Hormuz, and the Suez Canal. The analysis extends the classic “guns versus butter” framing by treating defence and health spending as co-evolving components of an interconnected fiscal-growth system. Using World Development Indicators data (1999-2024), trend slopes are estimated for military spending (% of GDP), healthcare spending (% of GDP), and GDP growth (annual %). Two derived indicators are computed, a defence-to-health slope ratio (military slope/health slope) and a fiscal-balance proxy (health slope …

Arum–D Nexus: Adaptive Reflexive Urban Metabolism For Complex Construction And Demolition Waste Governance In Bengaluru, Talat Naaz, Rosewine Joy

Northeast Journal of Complex Systems (NEJCS)

Urban material systems exhibit nonlinear dynamics governed by feedback, adaptation, and emergent coupling among institutions, markets, and behaviors. Construction and demolition (C&D) waste in Bengaluru is a great example of such complexity, where fragmented regulation, informal actors, and digital asymmetries coalesce into unstable waste flows and resource leakages. This study conceptualizes Bengaluru’s C&D waste system as a Complex Adaptive System (CAS), where institutional, market, behavioral, and metabolic subsystems co-evolve through nonlinear feedback interactions. A meta-analysis of secondary literature combined with benchmarking of government datasets is used to evaluate two key complexity indicators, i.e., response speed and feedback density. The advancement …

Solving Wordle Using Information Theory, Talal Aladaileh, Donald Stephens, Mallak Alqaisi, Congyu Wu

Northeast Journal of Complex Systems (NEJCS)

Wordle, a popular word-guessing game, challenges players to identify a five-letter secret word through iterative guesses and feedback on letter placement. The players must figure out the secret word within six guesses. After each guess, the letters will be color-coded based on different criteria. Optimizing the choice of guesses is critical for maximizing success within the limited attempts allowed. In this study, the application of Shannon entropy is explored as a strategy for selecting words that maximize information gain at each step of the game. By quantifying the uncertainty reduction achieved by potential guesses, this method prioritizes words that are …

A Multi-Layer Complex Adaptive System Framework For Ai-Driven Robo-Advisory Services, Jesty Mariam Philip, Mohit Boralkar, Alwin Joseph

Northeast Journal of Complex Systems (NEJCS)

The rapid integration of Artificial Intelligence (AI) into investment advisory services has changed financial decision-making, giving rise to adaptive robo-advisory systems capable of real-time analysis, personal recommendations, and autonomous portfolio optimization. Existing research evaluates these systems primarily through technological performance or investor adoption, overlooking the complex feedback-driven interactions that emerge when AI analytics, data environments, and human behavior operate together. This study addresses this gap by conceptualizing AI-enabled robo-advisors as a multi-layered Complex Adaptive System comprising historical data, real-time data, AI analytics, investor perception, and decision-making layers. A simulation model grounded in machine learning dynamics, behavioral finance, and complexity theory …

Regional Drought Modulation By Enso And Iod As Indicated By The Standardized Precipitation Index, Arpit Tiwari, Preethi Nanjundan, Tanu Sharma, Ravi Ranjan Kumar, Satyaban Bishoyi Ratna

Northeast Journal of Complex Systems (NEJCS)

Understanding the modulation of drought by large-scale ocean–atmosphere teleconnections is crucial for strengthening drought prediction and resilience in India. This study investigates the influence of the El Niño–Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD) on meteorological drought characteristics across India from 1950 to 2024 using the Standardized Precipitation Index (SPI) at a 12-month timescale. Drought events were quantified in terms of frequency, duration, severity, and intensity and linked to ENSO–IOD variability through composite, correlation, and mediation analyses. Results reveal that El Niño events consistently correspond to widespread and severe droughts, particularly over central and southern India, with drought …

Information Theory Analysis Of The Solar Wind Magnetic Structures For Space Weather Prediction, Katherine Holland

Doctoral Dissertations and Master's Theses

Forecasting space weather at Earth is highly complicated, because of the limited measurements of the dynamic processes in the Sun that span multiple temporal, spatial, and energy-scales. The solar wind is a highly structured, multi-scale, evolving plasma and consists of coronal mass ejections (CMEs), stream interaction regions (SIRs), expanding flux tubes (Borovsky, 2008), and interplanetary magnetic field (IMF) discontinuities and fluctuations. The aim of this research is to improve our understanding of the evolution and dissipation of different scale-size solar wind magnetic structures as they move from the Sun-Earth Lagrange point 1 (L1) to Earth's bow shock and, ultimately, to …

Optimal Control And Bifurcation Analysis Of A Predator–Prey Model With Self-Limiting Growth And Predator Disease, Dipo Aldila, Muhammad Akmal Fasya, Bevina D. Handari, Chidozie Williams Chukwu, Olumuyiwa James Peter

Mathematical Modelling and Numerical Simulation with Applications

We propose and analyze an eco-epidemiological predator–prey model that incorporates self-limitation and disease transmission within the predator population. The model is formulated as a system of ordinary differential equations describing logistic prey growth under the interspecific interaction with the predator. On the other hand, the predator population is divided into susceptible and infected classes, whose growth is constrained by prey availability. Three biologically relevant equilibria are identified: predator extinction, disease-free coexistence, and coexistence with endemic disease. The existence and stability of these equilibria are determined by key ecological and epidemiological thresholds, including the basic reproduction number. Using numerical continuation methods, …

Optimal Control Strategies For Infectious Diseases: A Numerical Simulation Approach, M. Abu Salek, Jannatun Nayeem, Romana Yesmin, M. Haider Ali Biswas, M. Humayun Kabir

Mathematical Modelling and Numerical Simulation with Applications

Various infectious diseases, such as Tuberculosis and Hepatitis B virus (HBV), caused by Mycobacterium bacteria and hepatitis B virus, respectively, pose serious threats worldwide. This paper examines the spread of these diseases using a mathematical model that incorporates control measures, including vaccination and awareness programs. We use a system of differential equations with control variables and apply Pontryagin's principle to determine optimal control strategies. The stability of the Disease Free Equilibrium (DFE) has been analysed and demonstrated to be both locally and globally asymptotically stable when the basic reproduction number remains below unity, thereby ensuring disease elimination. Furthermore, the Endemic …

Dynamical Analysis And Optimal Control Of The Mpox Transmission Model With Stratified Susceptibility, Tuhfatul Janan, Fatmawati Fatmawati, Cicik Alfiniyah, Santi Martini, Dipo Aldila, Agus Hasan

Mathematical Modelling and Numerical Simulation with Applications

This study develops a mathematical model of Mpox transmission that combines stratified susceptibility (low-risk and high-risk groups) with vaccinated and asymptomatically infected compartments. The analysis of the model begins with examining the well-posedness, boundedness, and nonnegativity conditions for the solutions. The local stabilities of the equilibria are examined through the Jacobian matrix and phase plane analysis, while the global stabilities are provided through Lyapunov functions. The estimated parameters are verified using epidemiological data on Mpox cases in the United States, with an MAPE of 2.20% and R_0 > 1, indicating that Mpox remains endemic. Sensitivity analysis indicates that the contact rate …

Assessing The Geomechanical Modelling Of Underground Reservoir For Co₂ Storage Trapping Mechanisms, Bonavian Hasiholan, Mohammed Ali Farea, Elhassan Mostafa Abdallah, Sami Abdelrahman M. Yagoub, Yasir Mukhtar

Mathematical Modelling and Numerical Simulation with Applications

Effective carbon dioxide (CO₂) storage is essential for mitigating climate change amid increasing global greenhouse gas emissions. This study investigates the influence of geomechanics on CO₂ storage performance within carbon capture and storage (CCS), focusing on structural, residual, and solubility trapping mechanisms using a fully coupled modeling framework. Two numerical models, with and without geomechanical effects, are developed to evaluate impacts on reservoir behavior, CO₂ migration, and trapping efficiency. Each mechanism is analyzed separately and within an integrated framework to assess their combined contributions. Results indicate that geomechanical coupling increases reservoir pressure, reduces CO₂ flow velocity, enhances migration control, and …

The Butterfly Effect In Economics: Exploring Chaos With A Simple Financial Model, Sandy Hs Herho

CODEE Journal

Wild swings in financial markets need not result from external shocks like earthquakes or wars—they can emerge from deterministic chaos. This article introduces kalimusada, an open-source Python library that lets students and instructors explore this phenomenon through a simple three- equation model of financial dynamics. The model couples interest rates, investment, and prices through nonlinear feedback, generating bounded but unpredictable oscillations characteristic of chaos. Tiny differences in starting conditions—smaller than any measurement could detect—grow exponentially until two initially identical economies follow completely different paths. The library provides ready-to-use tools for visualizing this “butterfly effect” in economics, computing divergence metrics, and …

Mathematicly Rigorous Quantum General Relativity, I: Pure, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

A pure quantum general relativity field is one lacking in matter. Such a field has a Lorentzian space-time geometry. A renormalized perturbation expansion, truncated to all finite orders, establishes  the existence of pure quantum general relativity with full mathematical rigor

Applications Of Machine Learning For Evaluating Downward-Coupled Stratosphere-Troposphere Interactions And Subseasonal Forecasts Of Opportunity, Elena M. Fernandez

Electronic Theses & Dissertations (2024 - present)

Wintertime stratospheric dynamics provide key information for understanding atmospheric teleconnections and improving subseasonal-to-seasonal (S2S) predictions on timescales of two weeks to two months. Periods of enhanced predictability, often referred to as forecasts of opportunity, arise from large-scale teleconnected variability, within which the stratosphere serves as an important precursor for tropospheric states, such as near-surface temperatures. While traditional diagnostics of downward coupled stratosphere-troposphere interactions typically rely on zonal-mean representations of wind and geopotential height, this dissertation presents an alternative vortex-centric framework through metrics that capture the daily geometric and dynamical evolution of the stratospheric polar vortex. The proposed stratospheric …

Quantum Mechanics As A Framework For Data Assimilation And Its Application To Atmospheric Parameterization, David Freeman

Dartmouth College Ph.D Dissertations

Quantum mechanics, as a mathematical system, can be understood as a generalization of classical probability theory. Quantum Mechanical Data Assimilation (QMDA) is a method in which classical dynamical systems are embedded into a quantum mechanical setting, with an associated data assimilation scheme leveraging the operator algebraic setting. In this dissertation, the algebraic structure underlying the operator theoretic formulation of QMDA is discussed. A procedure for closure of dynamical systems based on QMDA, known as Quantum Mechanical Closure (QMCl), is then constructed, and the procedures for constructing the quantum embeddings and implementing QMCl in practice are laid out and implemented for …

A Stability Analysis Of The Phase-Lock Equations, Brian M. Sunguza

UNF Graduate Theses and Dissertations

Ginzburg and Landau have provided a set of equations that relate superconductivity to magnetic fields. Through a transformation process, Zhan has derived what are now called the phase-lock equations. A stability analysis of the spatially-independent phase-lock equations is the purpose of this presentation. This simplification is significant since it allowed for the analytical determination of equilibria, their stability, and the influence of a periodic forcing function. Through the use of an original code, numerical simulations are shown to corroborate the analytical results described above.

This analysis includes novel Lyapunov functions that allowed for the analytical determination of the instability region. …