Research Interests

My primary research interests lie in the fields of Mathematical Biology, Nonlinear Dyanamics and Biostatistics. I am particularly fascinated by how mathematical and statistical models help us understand biological complexity across different scales from biomolecules to ecosystems.

I am particularly interested in how molecular-level processes-including gene expression variability, signalling noise, and drug interactions drive system-level behaviours such as tumor growth, cellular heterogeneity, and therapy resistance. A core focus of my research is to understand the statistical structure and biophysical constraints of models that capture these multiscale dynamics.

Keywords:

Mathematical Oncology Deterministic & Stochastic Modelling Nonlinear Dynamics Machine Learning-based Nonlinear Dynamics

Mathematical Oncology

I'm particularly interested in modelling how heterogeneous tumor cell populations and their spatial and architectural organization evolve under treatment and influence therapeutic response. My aim is to construct mathematical models and integrate with experimental and clinical data for patient-specific parameter inference and the construction of virtual patient cohorts, providing a framework for investigating and designing patient-specific treatment strategies.

Non-Linear Dynamics

Nonlinear dynamics studies systems where small changes can have disproportionately large effects, producing thresholds, oscillations, bistability and chaos. Many biological processes, from the cell cycle to circadian rhythms to gene regulation, behave this way, and tools like bifurcation analysis and stability theory help explain why.

Relevant papers
Emergence and Self-Organization of Periodic Structures in a Simple Ecological Model
Ruma Kumbhakar, Riddhiman Bhattacharya, N.C. Pati, Shilpa Garai, Nikhil Pal, Ranjit Kumar Upadhyay
[Preprint, 2026]
Dynamical Complexities of a Discrete-Time Prey-Predator Model with Fear and Its Carryover Effects
Sarbari Karmakar, Anirban Sen, Rumpaul Naj, Animesh Mahato, Riddhiman Bhattacharya, Nikhil Pal
[Preprint, 2026]

Machine Learning-based Nonlinear Dynamics

Machine learning has been used extensively to extract dynamical information directly from time-series data. One of our recent works focuses on data-driven estimation of Lyapunov exponents for nonlinear systems and using these estimates to efficiently characterize the dynamical behaviour of nonlinear systems under both single and simultaneous parameter variations. This approach efficiently captures chaotic and non-chaotic regions across parameter spaces, including the identification of periodic windows and organized periodic structures embedded within chaotic regimes.

Relevant papers
Machine Learning-Based Identification of Organized Periodic Structures in Chaotic Maps
Riddhiman Bhattacharya, Nibedita Nandi, Nikhil Pal
[Preprint, 2026]
Multistability and Machine Learning Based Characterization of the Parameter Space in a One-Dimensional Discrete Map
Riddhiman Bhattacharya, Deivasundari Muthukumar, Nibedita Nandi, Nikhil Pal, Karthikeyan Rajagopal, Sajad Jafari
[Preprint, 2026]

Another direction I'm interested in is the identification of governing nonlinear equations from available datasets by extracting dynamical relationships and parameter dependence directly from data. This provides a route towards more reliable parameter inference and the construction of less "sloppy" mathematical models. In particular, I'm interested in investigating how different model constructions that fit the same time-series data can lead to substantially different simulation behaviour, and in developing model identification approaches that favour dynamically reliable representations rather than simply exact fits to the available data.