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Dynamic Model for Life History of Scyphozoa.

Xie C, Fan M, Wang X, Chen M - PLoS ONE (2015)

Bottom Line: The combination of temperature increase, substrate expansion, and predator diminishment acts synergistically to create a habitat that is more favorable for jellyfishes.Reducing artificial marine constructions, aiding predator populations, and directly controlling the jellyfish population would help to manage the jellyfish blooms.The theoretical analyses and numerical experiments yield several insights into the nature underlying the model and shed some new light on the general control strategy for jellyfish.

View Article: PubMed Central - PubMed

Affiliation: School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, P. R. China; College of Science, Dalian Nationalities University, Dalian, Liaoning, P. R. China.

ABSTRACT
A two-state life history model governed by ODEs is formulated to elucidate the population dynamics of jellyfish and to illuminate the triggering mechanism of its blooms. The polyp-medusa model admits trichotomous global dynamic scenarios: extinction, polyps survival only, and both survival. The population dynamics sensitively depend on several biotic and abiotic limiting factors such as substrate, temperature, and predation. The combination of temperature increase, substrate expansion, and predator diminishment acts synergistically to create a habitat that is more favorable for jellyfishes. Reducing artificial marine constructions, aiding predator populations, and directly controlling the jellyfish population would help to manage the jellyfish blooms. The theoretical analyses and numerical experiments yield several insights into the nature underlying the model and shed some new light on the general control strategy for jellyfish.

No MeSH data available.


Related in: MedlinePlus

Phase portrait of system (2).(a) ad + bc > 0, c = 0. There are two equilibria with E0 being unstable and E1 being globally asymptotically stable. There is a heteroclinic orbit from E0 to E1. (b) ad + bc > 0, c ≠ 0. There are two equilibria with E0 being unstable and E* being globally asymptotically stable and there is a heteroclinic orbit from E0 to E*.
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pone.0130669.g002: Phase portrait of system (2).(a) ad + bc > 0, c = 0. There are two equilibria with E0 being unstable and E1 being globally asymptotically stable. There is a heteroclinic orbit from E0 to E1. (b) ad + bc > 0, c ≠ 0. There are two equilibria with E0 being unstable and E* being globally asymptotically stable and there is a heteroclinic orbit from E0 to E*.

Mentions: Let l = (∣a∣d + bc)/b1d. Then is positively invariant with respect to system (2). The Dulac’s criterion precludes the existence of nontrivial periodic solutions in Ω. System (2) possibly admits several different equilibrium states: extinction E0(0, 0), partial survival E1(a/b1, 0), and coexistence E*(P*, M*). The standard qualitative analysis techniques help to characterize the existence and stability of those equilibria and then the global dynamics of system (2) (see Table 2 for summarization and the S2 File for details of the proof).


Dynamic Model for Life History of Scyphozoa.

Xie C, Fan M, Wang X, Chen M - PLoS ONE (2015)

Phase portrait of system (2).(a) ad + bc > 0, c = 0. There are two equilibria with E0 being unstable and E1 being globally asymptotically stable. There is a heteroclinic orbit from E0 to E1. (b) ad + bc > 0, c ≠ 0. There are two equilibria with E0 being unstable and E* being globally asymptotically stable and there is a heteroclinic orbit from E0 to E*.
© Copyright Policy
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC4482707&req=5

pone.0130669.g002: Phase portrait of system (2).(a) ad + bc > 0, c = 0. There are two equilibria with E0 being unstable and E1 being globally asymptotically stable. There is a heteroclinic orbit from E0 to E1. (b) ad + bc > 0, c ≠ 0. There are two equilibria with E0 being unstable and E* being globally asymptotically stable and there is a heteroclinic orbit from E0 to E*.
Mentions: Let l = (∣a∣d + bc)/b1d. Then is positively invariant with respect to system (2). The Dulac’s criterion precludes the existence of nontrivial periodic solutions in Ω. System (2) possibly admits several different equilibrium states: extinction E0(0, 0), partial survival E1(a/b1, 0), and coexistence E*(P*, M*). The standard qualitative analysis techniques help to characterize the existence and stability of those equilibria and then the global dynamics of system (2) (see Table 2 for summarization and the S2 File for details of the proof).

Bottom Line: The combination of temperature increase, substrate expansion, and predator diminishment acts synergistically to create a habitat that is more favorable for jellyfishes.Reducing artificial marine constructions, aiding predator populations, and directly controlling the jellyfish population would help to manage the jellyfish blooms.The theoretical analyses and numerical experiments yield several insights into the nature underlying the model and shed some new light on the general control strategy for jellyfish.

View Article: PubMed Central - PubMed

Affiliation: School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, P. R. China; College of Science, Dalian Nationalities University, Dalian, Liaoning, P. R. China.

ABSTRACT
A two-state life history model governed by ODEs is formulated to elucidate the population dynamics of jellyfish and to illuminate the triggering mechanism of its blooms. The polyp-medusa model admits trichotomous global dynamic scenarios: extinction, polyps survival only, and both survival. The population dynamics sensitively depend on several biotic and abiotic limiting factors such as substrate, temperature, and predation. The combination of temperature increase, substrate expansion, and predator diminishment acts synergistically to create a habitat that is more favorable for jellyfishes. Reducing artificial marine constructions, aiding predator populations, and directly controlling the jellyfish population would help to manage the jellyfish blooms. The theoretical analyses and numerical experiments yield several insights into the nature underlying the model and shed some new light on the general control strategy for jellyfish.

No MeSH data available.


Related in: MedlinePlus