Dispersal-induced pattern-forming instabilities in host–parasitoid metapopulations

Ghorai, Santu; Chakraborty, Priyanka; Poria, Swarup; Bairagi, Nandadulal

doi:10.1007/s11071-020-05505-w

Cited by 11 publications

(6 citation statements)

References 61 publications

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“…According to ecologists, a habitat is seldom described by a torus but is widely used by mathematicians. For instance, this scenario is used to simulate spatio-temporal dynamics for continuous space (reaction-diffusion equations) [13,17,19] and for discrete space (ensembles of nonlinear oscillators) [2,12,14,18,31,32]. This range description is especially used in cellular automata and individual-based models [64,65].…”

Section: Population Dynamics Model With Age Structure and Simple Migr...mentioning

confidence: 99%

“…This phenomenon is simulated using various functions of coupling strength on distances between farther subpopulations. To analyze the conditions for the formation of various spatio-temporal structures (patterns), we rely on results and methodologies for studying dissipative structures observed in systems of nonlocally coupled nonlinear oscillators of various types [1,12,15,16,[26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

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Clustering Synchronization in a Model of the 2D Spatio-Temporal Dynamics of an Age-Structured Population with Long-Range Interactions

Кулаков

Frisman

2023

Mathematics

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The inhomogeneous population distribution appears as various population densities or different types of dynamics in distant sites of the extended habitat and may arise due to, for example, the resettlement features, the internal population structure, and the population dynamics synchronization mechanisms between adjacent subpopulations. In this paper, we propose the model of the spatio-temporal dynamics of two-age-structured populations coupled by migration (metapopulation) with long-range displacement. We study mechanisms leading to inhomogeneous spatial distribution as a type of cluster synchronization of population dynamics. To study the spatial patterns and synchronization, we use the method of constructing spatio-temporal profiles and spatial return maps. We found that patterns with spots or stripes are typical spatial structures with synchronous dynamics. In most cases, the spatio-temporal dynamics are mixed with randomly located single populations with strong burst (outbreak) of population size (solitary states). As the coupling parameters decrease, the number of solitary states grows, and they increasingly synchronize and form the clusters of solitary states. As a result, there are the several clusters with different dynamics. The appearance of these spatial patterns most likely occurs due to the multistability of the local age-structured population, leading to the spatio-temporal multistability.

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Section: Population Dynamics Model With Age Structure and Simple Migr...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Clustering Synchronization in a Model of the 2D Spatio-Temporal Dynamics of an Age-Structured Population with Long-Range Interactions

Кулаков

Frisman

2023

Mathematics

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“…Te reaction-difusion models can be further subdivided into continuous reaction-difusion models [12][13][14][15] and discrete reaction-difusion models [16,17]. In biomathematical models, continuous models can be used to describe organisms that are based on a large amount of data, but for organisms in which many movements and changes occur in discrete forms and the data collected and recorded are also in discrete forms; constructing discrete models to describe them will be more in line with objective reality such as host-parasitoid models.…”

Section: Introductionmentioning

confidence: 99%

“…Referring to the approach in the literature [1,2,16,17], we started to study the stability of the system (2) and (3). Let H n (i, j) � H n (i, j) − H * , P n (i, j) � P n (i, j) − P * , then (2) can be rewritten as follows:…”

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confidence: 99%

The Diffusion-Driven Instability for a General Time-Space Discrete Host-Parasitoid Model

Zhang

2023

Discrete Dynamics in Nature and Society

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In this paper, we consider a general time-space discrete host-parasitoid model with the periodic boundary conditions. We analyzed and obtained some usual conditions, such as Turing instability occurrence, Flip bifurcation occurrence, and Neimark-Sacker bifurcation occurrence. We also find several multiple bifurcation phenomena, such as 1 : 2 Resonance, Neimark-Sacker-Flip bifurcation, Neimark-Sacker-Neimark-Sacker bifurcation, Neimark-Sacker-Flip-Flip bifurcation, induced by diffusion. In a modified Nicholson-Bailey model, employing the mutual interference and diffusive interaction as bifurcation parameters, there appear route from standing Turing instability to multiple bifurcations by changing diffusive parameters. Some numerical simulations of the modified Nicholson-Bailey model support these corollaries.

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“…Particularly, the population model can be better described in discrete time and it is especially applicable in populations having non-overlapping generations, e.g., insect populations. Such discrete models are known to show richer dynamics compare to its continuous counterpart [24,25,26,27,28,29]. Thus, both from biological and dynamic point of views, study of discrete system is important.…”

Section: Introductionmentioning

confidence: 99%

Study of a discretized fractional-order eco-epidemiological model with prey infection

Mondal¹,

Cao²,

Bairagi³

2020

Fractional Differential Calculus

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In this paper, an attempt is made to understand the dynamics of a three-dimensional discrete fractional-order eco-epidemiological model with Holling type II functional response. We first discretize a fractional-order predator-prey-parasite system with piecewise constant arguments and then explore the system dynamics. Analytical conditions for the local stability of different fixed points have been determined using the Jury criterion. Several examples are given to substantiate the analytical results. Our analysis shows that stability of the discrete fractional order system strongly depends on the step-size and the fractional order. More specifically, the critical value of the step-size, where the switching of stability occurs, decreases as the order of the fractional derivative decreases. Simulation results explore that the discrete fractional-order system may also exhibit complex dynamics, like chaos, for higher step-size.

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Dispersal-induced pattern-forming instabilities in host–parasitoid metapopulations

Cited by 11 publications

References 61 publications

Clustering Synchronization in a Model of the 2D Spatio-Temporal Dynamics of an Age-Structured Population with Long-Range Interactions

Clustering Synchronization in a Model of the 2D Spatio-Temporal Dynamics of an Age-Structured Population with Long-Range Interactions

The Diffusion-Driven Instability for a General Time-Space Discrete Host-Parasitoid Model

Study of a discretized fractional-order eco-epidemiological model with prey infection

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