arXiv subjects

Chanaka Kottegoda

Publications and source records attributed to Chanaka Kottegoda.

5 recordsLinked to original sources

arXiv2026

Additional Food Enhances the Bifurcation Structure of Predator Competition Models

Additional food sources and predator competition are both known to impact the dynamics of predator-prey models. The Bazykin model of predator competition, with Holling type II functional response, possesses a rich bifurcation structure consisting of a focus-type degenerate Bogdanov-Takens bifurcation of codimension 3, and a degenerate Hopf bifurcation of codimension at most 2. Additional food models on the other hand are able to drive pest populations lower, with vast applicability in biological control. Despite these models being studied rigorously in the literature, the global bifurcation structure, of their possible complex dynamics, in a unified model, is unknown. In this work, we study an additional food model with generalized predator competition and Holling type-II functional response. Depending on the parameter values, the system can have up to three interior equilibria. Further, we show that this system exhibits a cusp-type (or focus-type) Bogdanov-Takens bifurcation of codimension at least 4 (or 3), a global Hopf bifurcation of codimension 3, and a homoclinic bifurcation of codimension 3. This shows there could exist three limit cycles around the BT point. These results demonstrate that additional food in Bazykin type models, can enhance their bifurcation structure. We discuss the applicability of these results to integrated pest management programs for the soybean aphid, wherein long term field data in the North-Central United States, shows two distinct limit cycles in aphid populations and their predators. Our results suggest biological control with additional food, is an effective management tactic for invasive pests.

q-bio.PE↗

arXiv2026

Oscillatory Regimes in a Game-Theoretic Model for Mosquito Population Dynamics under Breeding Site Control

Mosquito-borne diseases remain a major public-health threat, and the effective control of mosquito populations requires sustained household participation in removing breeding sites. While environmental drivers of mosquito oscillations have been extensively studied, the influence of spontaneous household decision-making on the dynamics of mosquito populations remains poorly understood. We introduce a game-theoretic model in which the fraction of households performing breeding site control evolves through imitation dynamics driven by perceived risks. Household behavior regulates the carrying capacity of the aquatic mosquito stage, creating a feedback between control actions and mosquito population growth. For a simplified model with constant payoffs, we characterize four locally stable equilibria, corresponding to full or no household control and the presence or absence of mosquito populations. When the perceived risk of not controlling breeding sites depends on mosquito prevalence, the system admits an additional equilibrium with partial household engagement. We derive conditions under which this equilibrium undergoes a Hopf bifurcation, yielding sustained oscillations arising solely from the interaction between mosquito abundance and household behavior. Numerical simulations and parameter explorations further describe the amplitude and phase properties of these oscillatory regimes.

math.DS↗

arXiv2025

An additional food driven biological control patch model, incorporating generalized competition

Additional food sources for an introduced predator are known to increase its efficiency on a target pest. In this context, inhibiting factors such as interference, predator competition, and the introduction of temporally dependent quantity and quality of additional food are all known to enable pest extinction. As climate change and habitat degradation have increasing effects in enhancing patchiness in ecological systems, the effect of additional food in patch models has also been recently considered. However, the question of complete pest extinction in such patchy systems remains open. In the current manuscript, we consider a biological control model where additional food drives competition among predators in one patch, and they subsequently disperse to a neighboring patch via drift or dispersal. We show that complete pest extinction in both patches is possible. Further, this state is proved to be globally asymptotically stable under certain parametric restrictions. We also prove a codimension-2 Bogdanov-Takens bifurcation. We discuss our results in the context of designing pest management strategies under enhanced climate change and habitat fragmentation. Such strategies are particularly relevant to control invasive pests such as the Soybean aphid (\emph{Aphis glycines}), in the North Central United States.

q-bio.PE↗

arXiv2025

Complex dynamics and pattern formation in a diffusive epidemic model with an infection-dependent recovery rate

A diffusive epidemic model with an infection-dependent recovery rate is formulated in this paper. Multiple constant steady states and spatially homogeneous periodic solutions are first proven by bifurcation analysis of the reaction kinetics. It is shown that the model exhibits diffusion-driven instability, where the infected population acts as an activator and the susceptible population functions as an in hibitor. The faster movement of the susceptible class will induce the spatial and spatiotemporal patterns, which are characterized by k-mode Turing instability and (k1,k2)-mode Turing-Hopf bifurcation. The transient dynamics from a purely temporal oscillatory regime to a spatial periodic pattern are discovered. The model reveals key transmission dynamics, including asynchronous disease recurrence, spatially patterned waves, and the formation of localized hotspots. The study suggests that spatially targeted strategies are necessary to contain disease waves that vary regionally and cyclically.

math.DS↗

arXiv2020

Multiple Limit Cycles and Heteroclinic Loops in a Predator-prey System with Allee Effects in Prey

The transition between strong and weak Allee effects in prey provides a simple regime shift in ecology. A deteriorating environment changes weak Allee effects into strong ones. In this paper, we study the interplay between the functional response of Holling type IV and both strong and weak Allee effects. The model investigated here presents complex dynamics and high codimension bifurcations. In particular, nilpotent cusp bifurcation, nilpotent saddle bifurcation and degenerate Hopf bifurcation of codimension 3 are completely analyzed, and the existence of homoclinic and heteroclinic loops are proven. Remarkably it is the first time that three limit cycles are discovered in predator-prey models with Allee effects. It turns out that strong Allee effects destabilize population dynamics, induce more regime shifts, decrease establishment likelihood of both species, increase vulnerability of ecosystem to collapse, while weak Allee effects promote sustained oscillations between predators and preys compared to systems without Allee effects. The theory developed here provides a sound foundation for understanding predator-prey interactions and biodiversity of species in natural systems.

math.DS↗