arXiv subjects

Sandip Saha

Publications and source records attributed to Sandip Saha.

13 recordsLinked to original sources

arXiv2025

Epigenetic feedback reshapes dynamical landscapes in gene regulatory networks

Understanding how gene regulatory networks (GRNs) give rise to stable and dynamic cellular states remains a central challenge in theoretical biology, particularly when slow epigenetic feedback reshapes the underlying regulatory landscape. While experimental approaches such as single-cell transcriptomics reveal rich dynamical behaviour, a tractable theoretical framework that links gene expression, epigenetic control, and collective dynamics remains challenging. Here, we develop an extended Dynamical Mean Field Theory (DMFT) framework for GRNs that incorporates epigenetic modifications as slow, feedback-driven variables. Building on the analogy between Hopfield networks and spin glass systems, we derive effective stochastic equations that reduce high-dimensional dynamics to a tractable form across multiple timescales. This formulation enables quantitative characterization of both stable and oscillatory regimes and reveals how epigenetic feedback reshapes the effective potential landscape governing cell fate decisions. Our model shows how epigenetic feedback regulation dynamically reshapes the Waddington landscape. Our results and methodology provide a unified theoretical framework for understanding developmental dynamics and epigenetic reprogramming in complex biological systems.

q-bio.MN↗

arXiv2025

Complex dynamics and route to quasiperiodic synchronization in non-isochronous directed Stuart-Landau triads

The coupled Stuart-Landau equation serves as a fundamental model for exploring synchronization and emergent behavior in complex dynamical systems. However, understanding its dynamics from a comprehensive nonlinear perspective remains challenging due to the multifaceted influence of coupling topology, interaction strength, and oscillator frequency detuning. Despite extensive theoretical investigations over the decades, numerous aspects remain unexplored, particularly those that bridge theoretical predictions with experimental observations-an essential step toward deepening our understanding of real-world dynamical phenomena. This work investigates the complex dynamics of unidirectionally coupled non-isochronous Stuart-Landau oscillators. Calculations of steady-states and their stability analysis further reveal that periodic attractors corresponding to weak forcing or coupling regimes are dynamically unstable, which pushes the system towards quasiperiodic oscillation on the torus attractor. The mapping of parameter values with the kind of attractor of the oscillatory system is presented and classified into periodic, quasiperiodic, partially synchronized, and chaotic regions. The results of this study can be leveraged to design complex yet controllable dynamical architectures.

nlin.AO↗

arXiv2025

Controlling complex rhythms: A hierarchical approach to limit cycle switching

Limit cycles are self-sustained, closed trajectories in phase space representing (un)-stable, periodic behavior in nonlinear dynamical systems. They underpin diverse natural phenomena, from neuronal firing patterns to engineering oscillations. The presence of multiple concentric limit cycles reflects distinct behavioral symmetries within a system. In this work, we investigate the hierarchical dynamical transitions from one limit cycle to another, driven by oscillatory excitation while preserving other system properties. We demonstrate that controlling multirhythmicity through hierarchical, stepwise periodic modulation enables reliable switching between rhythmic states. This hierarchical control framework is crucial for applications in neuro-engineering and synthetic biology, where precise, robust modulation of complex rhythmic behaviors enhances system functionality and adaptability.

nlin.AO↗

arXiv2024

Power Law Behavior of Center-Like Decaying Oscillation : Exponent through Perturbation Theory and Optimization

In dynamical systems theory, there is a lack of a straightforward rule to distinguish exact center solutions from decaying center-like solutions, as both require the damping force function to be zero [1, 2]. By adopting a multi-scale perturbative method, we have demonstrated a general rule for the decaying center-like power law behavior, characterized by an exponent of 1/3 . The investigation began with a physical question about the higher-order nonlinearity in a damping force function, which exhibits birhythmic and trirhythmic behavior under a transition to a decaying center-type solution. Using numerical optimization algorithms, we identified the power law exponent for decaying center-type behavior across various rhythmic conditions. For all scenarios, we consistently observed a decaying power law with an exponent of 1/3 .Our study aims to elucidate their dynamical differences, contributing to theoretical insights and practical applications where distinguishing between different types of center-like behaviour is crucial. This key result would be beneficial for studying the multi-rhythmic nature of biological and engineering systems.

math.DS↗

arXiv2022

Snoopy: A Webpage Fingerprinting Framework with Finite Query Model for Mass-Surveillance

Internet users are vulnerable to privacy attacks despite the use of encryption. Webpage fingerprinting, an attack that analyzes encrypted traffic, can identify the webpages visited by a user in a given website. Recent research works have been successful in demonstrating webpage fingerprinting attacks on individual users, but have been unsuccessful in extending their attack for mass-surveillance. The key challenges in performing mass-scale webpage fingerprinting arises from (i) the sheer number of combinations of user behavior and preferences to account for, and; (ii) the bound on the number of website queries imposed by the defense mechanisms (e.g., DDoS defense) deployed at the website. These constraints preclude the use of conventional data-intensive ML-based techniques. In this work, we propose Snoopy, a first-of-its-kind framework, that performs webpage fingerprinting for a large number of users visiting a website. Snoopy caters to the generalization requirements of mass-surveillance while complying with a bound on the number of website accesses (finite query model) for traffic sample collection. For this, Snoopy uses a feature (i.e., sequence of encrypted resource sizes) that is either unaffected or predictably affected by different browsing contexts (OS, browser, caching, cookie settings). Snoopy uses static analysis techniques to predict the variations caused by factors such as header sizes, MTU, and User Agent String that arise from the diversity in browsing contexts. We show that Snoopy achieves approximately 90% accuracy when evaluated on most websites, across various browsing contexts. A simple ensemble of Snoopy and an ML-based technique achieves approximately 97% accuracy while adhering to the finite query model, in cases when Snoopy alone does not perform well.

cs.CR↗

arXiv2021

Where the Liénard--Levinson--Smith (LLS) theorem cannot be applied for a generalised Liénard system

We have examined a class of Liénard--Levinson--Smith (LLS) system having a stable limit cycle which demonstrates the case where the LLS theorem cannot be applied. The problem has been partly raised in a recent communication by Saha et al., CNSNS 85, 105234 (2020) (last para of sec 4.2.2). Here we have provided a physical approach to address this problem using the concept of energy consumption per cycle. We have elaborated the idea through proper demonstration by considering a generalized model system. Such issues have potential utility in nonlinear vibration control.

nlin.AO↗

arXiv2020

Parametric excitation and Hopf bifurcation analysis of a time delayed nonlinear feedback oscillator

In this paper, an attempt has been made to understand the parametric excitation of a periodic orbit of nonlinear oscillator which can be a limit cycle, center or a slowly decaying center-type oscillation. For this a delay model is considered with nonlinear feedback oscillator defined in terms of Liénard oscillator description which can give rise to any one of the periodic orbits stated above. We have characterized the resonance and antiresonance behaviour for arbitrary nonlinear system from their stability and bifurcation analyses in reference to the standard delayed van der Pol system. An approximate analytical solution using Krylov--Bogoliubov (K-B) averaging method is utilised to recognize the sub-harmonic resonance and antiresonance, and average energy consumption per cycle. Direction of Hopf bifurcation and stability of the periodic solution bifurcating from the trivial fixed point are carried out using normal form and center manifold theory. The parametric excitation is also thoroughly investigated via bifurcation analysis to find the role of the control parameters like time delay, damping and nonlinear terms.

nlin.CD↗

arXiv2020

Suppressing birhythmicity by parametrically modulating nonlinearity in limit cycle oscillators

Multirhythmicity, a form of multistability, in an oscillator is an intriguing phenomenon found across many branches of science. From an application point of view, while the multirhythmicity is sometimes desirable as it presents us with many possible coexisting stable oscillatory states to tap into, it can also be a nuisance because a random perturbation may make the system settle onto an unwanted stable state. Consequently, it is not surprising that there are many natural and artificial mechanisms available that can control the multirhythmicity. We propose in this paper the idea of incorporating parametric (periodic) modulation of the nonlinear damping in the limit cycle oscillators with a view to exciting resonance and antiresonance responses at particular angular driving frequencies, and controlling the resulting birhythmicity by changing the amplitude of the modulation. To this end, we employ analytical (perturbative) and numerical techniques on the van der Pol oscillator---a paradigmatic limit cycle system---having additional position dependent time delay term and its modified autonomous birhythmic version. We also bring the fact to the fore that introduction of delay---a commonly adopted method of controlling multirhythmicity---in such a system can sometimes bring forth unwanted birhythmicity; and interestingly, our method of controlling birhythmicity through periodic modulation can suppress such a delay induced birhythmic response.

nlin.AO↗

arXiv2020

Systematic designing of bi-rhythmic and tri-rhythmic models in families of Van der Pol and Rayleigh oscillators

Van der Pol and Rayleigh oscillators are two traditional paradigms of nonlinear dynamics. They can be subsumed into a general form of Liénard--Levinson--Smith(LLS) system. Based on a recipe for finding out maximum number of limit cycles possible for a class of LLS oscillator, we propose here a scheme for systematic designing of generalised Rayleigh and Van der Pol families of oscillators with a desired number of multiple limit cycles. Numerical simulations are explicitly carried out for systematic search of the parameter space for bi-rhythmic and tri-rhythmic systems and their higher order variants.

nlin.AO↗

arXiv2020

A Genetic Algorithm based Kernel-size Selection Approach for a Multi-column Convolutional Neural Network

Deep neural network-based architectures give promising results in various domains including pattern recognition. Finding the optimal combination of the hyper-parameters of such a large-sized architecture is tedious and requires a large number of laboratory experiments. But, identifying the optimal combination of a hyper-parameter or appropriate kernel size for a given architecture of deep learning is always a challenging and tedious task. Here, we introduced a genetic algorithm-based technique to reduce the efforts of finding the optimal combination of a hyper-parameter (kernel size) of a convolutional neural network-based architecture. The method is evaluated on three popular datasets of different handwritten Bangla characters and digits. The implementation of the proposed methodology can be found in the following link: https://github.com/DeepQn/GA-Based-Kernel-Size.

cs.CV↗

arXiv2019

Reduction of Kinetic Equations to Liénard-Levinson-Smith Form: Counting Limit Cycles

We have presented an unified scheme to express a class of system of equations in two variables into a Liénard-Levinson-Smith (LLS) oscillator form. We have derived the condition for limit cycle with special reference to Rayleigh and Liénard systems for arbitrary polynomial functions of damping and restoring force. Krylov-Boguliubov (K-B) method is implemented to determine the maximum number of limit cycles admissible for a LLS oscillator atleast in the weak damping limit. Scheme is illustrated by a number of model systems with single cycle as well as the multiple cycle cases.

math.DS↗

arXiv2018

When an oscillating center in an open system undergoes power law decay

We have probed the condition of periodic oscillation in a class of two variable nonlinear dynamical open systems modeled with Lienard-Levinson-Smith(LLS) equation which can be a limit cycle, center or a very slowly decaying center type oscillation. Using a variety of examples of open systems like Glycolytic oscillator, Lotka-Volterra(L-V) model, a generalised van der Pol oscillator and a time delayed nonlinear feedback oscillation as a non-autonomous system, each of which contains a family of periodic orbits, we have solved LLS systems in terms of a multi-scale perturbation theory using Krylov-Bogoliubov(K-B) method and it is utilised to characterise the size and shape of the limit cycle and center as well as the approach to their steady state dynamics. We have shown the condition when the average scaled radius of a center undergoes a power law decay with exponent 1/2.

nlin.CD↗

arXiv2018

Isochronicity and limit cycle oscillation in chemical systems

Chemical oscillation is an interesting nonlinear dynamical phenomenon which arises due to complex stability condition of the steady state of a reaction far away from equilibrium which is usually characterised by a periodic attractor or a limit cycle around an interior stationary point. In this context Lienard equation is specifically used in the study of nonlinear dynamical properties of an open system which can be utilized to obtain the condition of limit cycle. In conjunction with the property of limit cycle oscillation, here we have shown the condition for isochronicity for different chemical oscillators with the help of renormalisation group method with multiple time scale analysis from a Lienard system. When two variable open system of equations are transformed into a Lienard system of equation the condition for limit cycle and isochronicity can be stated in a unified way. For any such nonlinear oscillator we have shown the route of a dynamical transformation of a limit cycle oscillation to a periodic orbit of centre type depending on the parameters of the system.

math.DS↗