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Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest…
Recent progress in diverse intelligence has shown simple learning capacities below the organism level - single cells and even molecular networks. However, there are still many knowledge gaps around learning capacity above the organism…
In this paper, conformal fractional order discretization [20, 24, 25] is used to analyze bifurcation analysis and stability of a predator-prey system. A continuous model has been discretized into a discrete one while preserving the…
The effect of demographic stochasticity, in the form of Gaussian white noise, in a predator-prey model with one fast and two slow variables is studied. We derive the stochastic differential equations (SDEs) from a discrete model. For…
We introduce and study a stochastic model for the dynamics of colonial species, which reproduce through fission or fragmentation. The fission rate depends on the relative sizes of colonies in the population, and the growth rate of colonies…
We report on the dynamics of collective alignment in groups of the cichlid fish, Etroplus suratensis. Focusing on small-to-intermediate sized groups ($10<N<100$), we demonstrate that schooling (highly polarised and coherent motion) is…
Mathematical modeling based on time-delay differential equations is an important tool to study the role of delay in biological systems and to evaluate its impact on the asymptotic behavior of their dynamics. Delays are indeed found in many…
Behavior analysis of animals involves the observation of intraspecific and interspecific interactions among various organisms in the environment. Collective behavior such as herding in farm animals, flocking of birds, and shoaling and…
While a rich variety of self-propelled particle models propose to explain the collective motion of fish and other animals, rigorous statistical comparison between models and data remains a challenge. Plausible models should be flexible…
Understanding the training dynamics of deep learning models is perhaps a necessary step toward demystifying the effectiveness of these models. In particular, how do data from different classes gradually become separable in their feature…
In order to understand the impact of random influences at physical boundary on the evolution of multiscale systems, a stochastic partial differential equation model under a fast random dynamical boundary condition is investigated. The…
In traditional harvesting model a fishing effort E is defined by the fishing intensity and does not address the inverse effect of fish abundance on the fishing effort. In this paper, based on a canonical differential equation model, we…
This paper formulates two 3D stochastic differential equations (SDEs) of two microbial populations in a chemostat competing over a single substrate. The two models have two distinct noise sources. One is general noise whereas the other is…
The spatio-temporal dynamics of three interacting species, two preys and one predator, in the presence of two different kinds of noise sources is studied. To describe the spatial distributions of the species we use a model based on…
Understanding and predicting interactions between predators and prey and their environment are fundamental for understanding food web structure, dynamics, and ecosystem function in both terrestrial and marine ecosystems.Thus, estimating the…
When training data are fragmented across batches or federated-learned across different geographic locations, trained models manifest performance degradation. That degradation partly owes to covariate shift induced by data having been…
Quantifying fish community structure is essential for understanding biodiversity and ecosystem responses in a changing environment, yet existing survey methods provide limited high-frequency, quantitative observations. Conventional…
Noise induced changes in the critical and oscillatory behavior of a Prey-Predator system are studied using power spectrum density and Spectral Amplification Factor (SAF) analysis. In the absence of external noise, the population densities…
Animals form groups for many reasons but there are costs and benefit associated with group formation. One of the benefits is collective memory. In groups on the move, social interactions play a crucial role in the cohesion and the ability…
This paper addresses the estimation of a dynamic interaction network, a network of influence among individuals, under projected visual stimuli to quantify the influences of inter-individual interactions and external stimuli on collective…