arXiv subjects

Cris R. Hasan

Publications and source records attributed to Cris R. Hasan.

4 recordsLinked to original sources

arXiv2026

A multi-objective optimization framework for sustainable transitions

Achieving a just and sustainable transition requires the pursuit of multiple social and environmental targets. Two primary barriers impede this process: (1) targets are often in conflict with each other, and (2) policies aimed at these targets are commonly planned in isolation, neglecting complex interdependencies in the system. To address these challenges, we propose a general modeling framework that evaluates the holistic impact of policies and decision-making on sustainability targets while capturing system interdependencies in a policy-target network. Inspired by Kauffman's NK fitness landscape, our framework takes the form of a multi-objective optimization model that employs a dynamic evolutionary algorithm in conjunction with network analysis. Our algorithm accounts for tradeoffs between conflicting targets by dynamically reallocating resources to the most impactful and efficient policies. One key finding indicates that increasing resources generally enhances performance, but marginal gains stagnate at a point of diminishing returns. Sensitivity analysis reveals that the system is primarily driven by three factors: budget constraint, network density (interconnectivity), and policy efficacy. This study serves as a foundational step towards developing a decision-support tool that assists policymakers in achieving optimal outcomes for problems with a large number of dynamically interacting targets.

math.DS↗

arXiv2023

Rate-Induced Tipping in Heterogeneous Reaction-Diffusion Systems: An Invariant Manifold Framework and Geographically Shifting Ecosystems

We propose a framework to study tipping points in reaction-diffusion equations (RDEs) in one spatial dimension, where the reaction term decays in space (asymptotically homogeneous) and varies linearly with time (nonautonomous) due to an external input. A compactification of the moving-frame coordinate together with Lin's method to construct heteroclinic orbits along intersections of stable and unstable invariant manifolds allows us to (i) obtain multiple coexisting pulse and front solutions for the RDE by computing heteroclinic orbits connecting equilibria at negative and positive infinity in the compactified moving-frame ordinary differential equation, (ii) detect tipping points as dangerous bifurcations of such heteroclinic orbits, and (iii) obtain tipping diagrams by numerical continuation of such bifurcations. We apply our framework to an illustrative model of a habitat patch that features an Allee effect in population growth and is geographically shrinking or shifting due to human activity or climate change. Thus, we identify two classes of tipping points to extinction: bifurcation-induced tipping (B-tipping) when the shrinking habitat falls below some critical length and rate-induced tipping (R-tipping) when the shifting habitat exceeds some critical speed. We explore two-parameter R-tipping diagrams to understand how the critical speed depends on the size of the habitat patch and the dispersal rate of the population, uncover parameter regions where the shifting population survives, and relate these regions to the invasion speed in an infinite homogeneous habitat. Furthermore, we contrast the tipping instabilities with gradual transitions to extinction found for logistic population growth without the Allee effect.

math.DS↗

arXiv2021

Numerical continuation of spiral waves in heteroclinic networks of cyclic dominance

Heteroclinic-induced spiral waves may arise in systems of partial differential equations that exhibit robust heteroclinic cycles between spatially uniform equilibria. Robust heteroclinic cycles arise naturally in systems with invariant subspaces and their robustness is considered with respect to perturbations that preserve these invariances. We make use of particular symmetries in the system to formulate a relatively low-dimensional spatial two-point boundary-value problem in Fourier space that can be solved efficiently in conjunction with numerical continuation. The standard numerical set-up is formulated on an annulus with small inner radius, and Neumann boundary conditions are used on both inner and outer radial boundaries. We derive and implement alternative boundary conditions that allow for continuing the inner radius to zero and so compute spiral waves on a full disk. As our primary example, we investigate the formation of heteroclinic-induced spiral waves in a reaction-diffusion model that describes the spatiotemporal evolution of three competing populations in a two-dimensional spatial domain--much like the Rock-Paper-Scissors game. We further illustrate the efficiency of our method with the computation of spiral waves in a larger network of cyclic dominance between five competing species, which describes the so-called Rock-Paper-Scissors-Lizard-Spock game.

math.AP↗

arXiv2021

Spatiotemporal stability of periodic travelling waves in a heteroclinic-cycle model

We study a Rock-Paper-Scissors model for competing populations that exhibits travelling waves in one spatial dimension and spiral waves in two spatial dimensions. A characteristic feature of the model is the presence of a robust heteroclinic cycle that involves three saddle equilibria. The model also has travelling fronts that are heteroclinic connections between two equilibria in a moving frame of reference, but these fronts are unstable. However, we find that large-wavelength travelling waves can be stable in spite of being made up of three of these unstable travelling fronts. In this paper, we focus on determining the essential spectrum (and hence, stability) of large-wavelength travelling waves in a cyclic competition model with one spatial dimension. We compute the curve of transitions from stability to instability with the continuation scheme developed by Rademacher et al. (2007 Physica D 229 166-83). We build on this scheme and develop a method for computing what we call belts of instability, which are indicators of the growth rate of unstable travelling waves. Our results from the stability analysis are verified by direct simulation for travelling waves as well as associated spiral waves. We also show how the computed growth rates accurately quantify the instabilities of the travelling waves.

nlin.PS↗