For a family of non-autonomous differential equations with distributed delays, we give sufficient conditions for the global exponential stability of an equilibrium point. This family includes most of the delayed models of neural networks of Hopfield type, with time-varying coefficients and distributed delays. For these models, we establish sufficient conditions for their global exponential stability. The existence and global exponential stability of a periodic solution is also addressed. A comparison of results shows that these results are general, news, and add something new to some earlier publications.

a b s t r a c tFor a general Cohen-Grossberg neural network model with potentially unbounded timevarying coefficients and infinite distributed delays, we give sufficient conditions for its global asymptotic stability. The model studied is general enough to include, as subclass, the most of famous neural network models such as Cohen-Grossberg, Hopfield, and bidirectional associative memory. Contrary to usual in the literature, in the proofs we do not use Lyapunov functionals. As illustrated, the results are applied to several concrete models studied in the literature and a comparison of results shows that our results give new global stability criteria for several neural network models and improve some earlier publications.

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The purpose of this study is to investigate the factors that affect the Nonprofit Organization’s (NPO) competencies and leadership in a crisis situation, specifically in the Portuguese NPOs during COVID-19. Adopting an interdisciplinary perspective, this article integrates crisis management literature with leadership literature. Highlighting the leadership perspective of both intermediate employees (technical director) and top management (executive director), this research aims to advance knowledge on the main organizational leadership competencies that NPOs need to have to better cope with crises. One hundred and seventy-four (174) NPOs representatives voluntarily participated in the study which involved a survey questionnaire based on a five-point Likert scale for 23 items included in the questionnaire. Principal component analysis using varimax rotation was applied to reduce the number of variables. Reliability tests were performed to assess the items included in the questionnaire. Tests included test-retest reliability, Cronbach alpha, and split-half reliability coefficients. Results show that the most important factors that improve the capability of a NPO to cope with a crisis are: respond to all stakeholders through accountability, plan based on identification of vulnerabilities, and build a foundation of trust through communication. Additionally, it is possible to suggest that staff and top management perceive crisis and leadership competencies differently. It is possible to conclude, that these factors can be used as important lines of action to structure the sustainable development and planning of NPOs’ strategies of other similar crisis to come in the future. Findings, the implications of this work, and avenues for future NPOs crisis management and leadership research are addressed.

In this article we introduce a one-parameter family of skew product (Gt) t∈[− , ] maps exhibiting a heterodimensional cycle such that the number of isolated periodic orbits inside it has not super-exponential growth. The dynamics in the central direction of the maps Gt is described by a one-parameter family of system of iterated functions.