| Abstract: |
| This talk aims to discuss a novel consumer-resource system, which incorporates resource decay and consumer loss as well as the resource diffusion, under conditions that the resource input rate may exhibit spatial heterogeneity and temporal periodicity. Our findings show two sharply contrasting dynamical regimes: (i) for the immobile resource case, the resource remains limited at locations where it decays, while exhibits infinite-time blow-up at locations where it does not decay either when the consumer population becomes extinct, or for the high yield rates when the consumer population persists; (ii) in contrast, a mobile resource remains globally bounded for all time unconditionally. These results highlight the pivotal role of the resource decay and motility in suppressing blow-up phenomena, thereby offering a new understanding for the consumer-resource interaction in real ecological systems. |
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