arXiv:2510.04501v2 Announce Type: replace-cross
Abstract: We investigate traveling wave solutions in the two-species reaction-diffusion Lotka-Volterra competition system under weak competition. For the strict weak competition regime $(b0)$, we construct refined upper and lower solutions combined with the Schauder fixed point theorem to establish the existence of traveling waves for all wave speeds $sgeq s^*:=max2,2sqrtad$, and provide verifiable sufficient conditions for the emergence of non-monotone waves. Such conditions for non-monotonic waves have not been explicitly addressed in previous studies. It is interesting to point out that our result for non-monotone waves also hold for the critical speed case $s=s^*$. In addition, in the critical weak competition case $(b0)$, we rigorously prove, for the first time, the existence of front-pulse traveling waves.
Generative AI-assisted Participatory Modeling in Socio-Environmental Planning under Deep Uncertainty
arXiv:2603.17021v1 Announce Type: new Abstract: Socio-environmental planning under deep uncertainty requires researchers to identify and conceptualize problems before exploring policies and deploying plans. In practice