Spatial movement with distributed memory

Shi, Qingyan; Shi, Junping; Wang, Hao

doi:10.1007/s00285-021-01588-0

Cited by 44 publications

(28 citation statements)

References 47 publications

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“…In the scenario outlined above, the inclusion of time delays is purely discrete in the sense that the agents remember only exactly τ units ago. As previously suggested, it is more realistic to instead consider a distribution over all previous times, though it becomes more significantly more technical than each of the previous models [55]. Before introducing the model itself, it is instructive to first explore the following spatiotemporal convolution kernel :…”

Section: Distributed Time Delaysmentioning

confidence: 99%

“…In [55], the waning of memory due to the passage of time is considered through a Gamma distribution, with two specific cases referred to as a weak or strong kernel, respectively:…”

Section: Distributed Time Delaysmentioning

confidence: 99%

“…[59] does not consider the existence of solutions to problem (2.23), and so this is an open question. [55] does not explicitly consider the existence of solutions to model (2.27), however [55, Lemma 2.2] (the statement of which is found in the Appendix B.3.2) provides an interesting equivalence result between the delay differential equations and a certain form of Keller-Segel chemotaxis model. Hence, existence and non-existence of solutions may follow from the vast literature concerning Keller-Segel type systems.…”

Section: B12 Explicit Memory Modelsmentioning

confidence: 99%

“…where G is the Green's function for the heat equation in Ω subject to homogeneous Neumann boundary data, and G is either the weak or strong kernel defined in (2.26). We first state Lemma 2.1 found in [55].…”

Section: A2 Derivation Of Space Use Coefficients From Utilization Dis...mentioning

confidence: 99%

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Open problems in PDE models for knowledge-based animal movement via nonlocal perception and cognitive mapping

Wang¹,

Salmaniw²

2022

Preprint

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The inclusion of cognitive processes, such as perception, learning and memory, are inevitable in mechanistic animal movement modelling. Cognition is the unique feature that distinguishes animal movement from mere particle movement in chemistry or physics. Hence, it is essential to incorporate such knowledge-based processes into animal movement models. We summarize popular deterministic mathematical models derived from first principles and their rigorous analyses. Mathematical rules of thumb will be provided to judge the model rationality. We will briefly present available mathematical techniques and introduce useful measures of success to compare and contrast the possible outcomes. Throughout the review, we propose future mathematical challenges and development in the form of open questions. This topic is timely and cutting-edge in applied mathematics with many intriguing directions to be explored.

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Section: Distributed Time Delaysmentioning

confidence: 99%

“…In [55], the waning of memory due to the passage of time is considered through a Gamma distribution, with two specific cases referred to as a weak or strong kernel, respectively:…”

Section: Distributed Time Delaysmentioning

confidence: 99%

Section: B12 Explicit Memory Modelsmentioning

confidence: 99%

Section: A2 Derivation Of Space Use Coefficients From Utilization Dis...mentioning

confidence: 99%

See 2 more Smart Citations

Open problems in PDE models for knowledge-based animal movement via nonlocal perception and cognitive mapping

Wang¹,

Salmaniw²

2022

Preprint

Self Cite

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show abstract

“…Recently, there has been an increasing activity and interest on the dynamics of the single population model with memory-based diffusion. [6][7][8][9][10] It has been shown in Ref. 5 that the stability of a spatially homogeneous steady state fully depends on the reaction term and the ratio of the two diffusion coefficients but is independent of the memory delay, whereas the cooperation of both memory delay and maturation delay can affect the stability of a spatially homogeneous steady state.…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal dynamics of a diffusive consumer‐resource model with explicit spatial memory

2021

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Spatial memory is inevitable in animal movement modeling but elusive in many classical models. A nonlocal integral term involving space is a traditional way to incorporate spatial memory, but the actual spatial memory should depend on past information so that delay naturally arises. We propose a new consumer-resource model with random and memory-based diffusions in which the resource species has no memory or cognition, whereas the consumer species has spatial memory. By using the memory-based diffusion coefficient and the averaged memory period of the consumer as the control parameters, we find Hopf bifurcations and stability switches occur and spatially nonhomogeneous periodic solutions are generated. It is well known that prey-taxis enhances the stability of a homogeneous coexistence state in a predator-prey system, and here we show that memory-based prey-taxis can destabilize a constant coexistence and generate complex spatiotemporal pattern formation. Using the obtained theoretical results,

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Dynamical analysis of a spatial memory prey–predator system with gestation delay and strong Allee effect

Ye,

Zhao,

2024

Z. Angew. Math. Phys.

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Spatial movement with distributed memory

Cited by 44 publications

References 47 publications

Open problems in PDE models for knowledge-based animal movement via nonlocal perception and cognitive mapping

Open problems in PDE models for knowledge-based animal movement via nonlocal perception and cognitive mapping

Spatiotemporal dynamics of a diffusive consumer‐resource model with explicit spatial memory

Dynamical analysis of a spatial memory prey–predator system with gestation delay and strong Allee effect

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