scholarly journals When Are Mixed Equilibria Relevant?

2019 ◽  
Author(s):  
Daniel Friedman ◽  
shuchen zhao
Keyword(s):  
2017 ◽  
Vol 284 (1868) ◽  
pp. 20171192 ◽  
Author(s):  
A.-S. Lafuite ◽  
C. de Mazancourt ◽  
M. Loreau

Natural habitat destruction and fragmentation generate a time-delayed loss of species and associated ecosystem services. As social–ecological systems (SESs) depend on a range of ecosystem services, lagged ecological dynamics may affect their long-term sustainability. Here, we investigate the role of consumption changes for sustainability, under a time-delayed ecological feedback on agricultural production. We use a stylized model that couples the dynamics of biodiversity, technology, human demography and compliance with a social norm prescribing sustainable consumption. Compliance with the sustainable norm reduces both the consumption footprint and the vulnerability of SESs to transient overshoot-and-collapse population crises. We show that the timing and interaction between social, demographic and ecological feedbacks govern the transient and long-term dynamics of the system. A sufficient level of social pressure (e.g. disapproval) applied on the unsustainable consumers leads to the stable coexistence of unsustainable and sustainable or mixed equilibria, where both defectors and conformers coexist. Under bistability conditions, increasing extinction debts reduces the resilience of the system, thus favouring abrupt regime shifts towards unsustainable pathways. Given recent evidence of large extinction debts, such results call for farsightedness and a better understanding of time delays when studying the sustainability of coupled SESs.


Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 270 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Mihai Postolache ◽  
Ching-Feng Wen ◽  
Yonghong Yao

Multistep composite implicit and explicit extragradient-like schemes are presented for solving the minimization problem with the constraints of variational inclusions and generalized mixed equilibrium problems. Strong convergence results of introduced schemes are given under suitable control conditions.


2004 ◽  
Vol 118 (1) ◽  
pp. 61-79 ◽  
Author(s):  
Federico Echenique ◽  
Aaron Edlin

2016 ◽  
Vol 17 (2) ◽  
pp. 547-579 ◽  
Author(s):  
Xia Yang ◽  
Xuegang Jeff Ban ◽  
Rui Ma

2014 ◽  
Vol 2014 ◽  
pp. 1-25 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Suliman Al-Homidan

We introduce new implicit and explicit iterative algorithms for finding a common element of the set of solutions of the minimization problem for a convex and continuously Fréchet differentiable functional, the set of solutions of a finite family of generalized mixed equilibrium problems, and the set of solutions of a finite family of variational inclusions in a real Hilbert space. Under suitable control conditions, we prove that the sequences generated by the proposed algorithms converge strongly to a common element of three sets, which is the unique solution of a variational inequality defined over the intersection of three sets.


2014 ◽  
Vol 2014 ◽  
pp. 1-26 ◽  
Author(s):  
A. E. Al-Mazrooei ◽  
A. Latif ◽  
J. C. Yao

We propose implicit and explicit iterative algorithms for finding a common element of the set of solutions of the minimization problem for a convex and continuously Fréchet differentiable functional, the set of solutions of a finite family of generalized mixed equilibrium problems, and the set of solutions of a finite family of variational inequalities for inverse strong monotone mappings in a real Hilbert space. We prove that the sequences generated by the proposed algorithms converge strongly to a common element of three sets, which is the unique solution of a variational inequality defined over the intersection of three sets under very mild conditions.


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