Stability and Hopf Bifurcation of a Stage-Structured Cannibalism Model with Two Delays

In this work, we consider a stage-structured cannibalism model with two delays. One delay characterizes the lag effect of negative feedback of the prey species, the other has the effect of gestation of the adult predator population. Firstly, criteria for the local stability of feasible equilibria are established. Meanwhile, by choosing delay as a bifurcation parameter, the criteria on the existence of Hopf bifurcation are established. Furthermore, by the normal form theory and center manifold theorem, we derive the explicit formulas determining the properties of periodic solutions. Finally, the theoretical results are illustrated by numerical simulations, from which we can see that the predator’s gestation time delay can make the chaotic phenomenon disappear and maintain periodic oscillation, and that a large feedback time delay of prey can make predators extinct and prey form a periodic solution.

To Leverage the Innovation Capability by Co-creation of Human-Machine

Although a societal consensus has been reached about the partnership between human beings and smart machines, limited research has been carried out to consider advances in its combination pattern, function mechanism, and developing creativity. Based on occurred disruptive changes form theory to practice, a new paradigm of co-creation by synergistic human-machine is proposed, which refers to that interaction of human-machine learning in a holistic system increase complementarity of abilities and integration of wisdom to realize an augmented synergy made up of hybrid intelligences. This augmented intelligence can effectively account for shifts in business logic and the productive solutions to the multiple complex problems during smart manufacturing. It has been discovered that the positive consequences of synergistic human-machine co-creation include not only sustainable labor patterns, but the ability to overcome multiple complexities and steadily increase business value. All this is further elaborated in the Baizhentang Foods case. This paper discusses the main prospects of the theoretical developments presented here for future research on organizational behavior and a synergistic human-machine structure.

Hopf Bifurcation Analysis of a Two-Delay HIV-1 Virus Model with Delay-Dependent Parameters

In this paper, a two-delay HIV-1 virus model with delay-dependent parameters is considered. The model includes both virus-to-cell and cell-to-cell transmissions. Firstly, immune-inactivated reproduction rate R 0 and immune-activated reproduction rate R 1 are deduced. When R 1 > 1 , the system has the unique positive equilibrium E ∗ . The local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analyzing the characteristic equation at the positive equilibrium with the time delay as the bifurcation parameter and four different cases. Besides, we obtain the direction and stability of the Hopf bifurcation by using the center manifold theorem and the normal form theory. Finally, the theoretical results are validated by numerical simulation.

The Lives of Marx: Hägglund and Marx’s Philosophy after Pippin and Postone

To make ‘philosophy worldly’ often requires an act of translation. In This Life, Martin Hägglund argues for the relevance of Marx to our contemporary lives. By way of a lively and sophisticated dialogue between philosophical interlocutors – including Hegel and Marx – Hägglund offers a compelling account of the relation between time, value and freedom. This Life translates current issues in academic philosophy into a popular register that does not reduce the complexity of the issues but shows what is at stake for our own lives. Hägglund provides a synthesis of Robert B. Pippin’s normative reading of Hegel and the value-form critical theory of Moishe Postone’s Marxism. Further, Hägglund’s vision of freedom outflanks the political limitations of Pippin’s Hegel and Postone’s Marx while retaining the power of their analyses. I assess his interpretation of Hegel and critically examine the concept of value operative in This Life, and frame this question in terms of value-form theory.

Stability and Hopf Bifurcation Analysis of a Delayed Innovation Diffusion Model with Intra-Specific Competition

This article is concerned with the diffusion of a sport in a region, and the innovation diffusion model comprising of population classes, viz. nonadopters class, information class and adopters class. A qualitative analysis is carried out to assess the global asymptotic stability of the interior equilibrium for null delay. It has also been proved that the parameter [Formula: see text] (age gaps among sportspersons) in the intra-specific competition between the new players and the senior players can even destabilize the otherwise globally stable interior equilibrium state and the coexistence of all the populations is possible through periodic solutions due to Hopf bifurcation. With the help of normal form theory and center manifold arguments, the stability of bifurcating periodic orbits is determined. Numerical simulations have been executed in support of the analytical findings.

p-form surface charges on AdS: renormalization and conservation

Surface charges of a p-form theory on the boundary of an AdSd+1 spacetime are computed. Counter-terms on the boundary produce divergent corner-terms which holographically renormalize the symplectic form. Different choices of boundary conditions lead to various expressions for the charges and the associated fluxes. With the usual standard AdS boundary conditions, there are conserved zero-mode charges. Moreover, we explore two leaky boundary conditions which admit an infinite number of charges forming an Abelian algebra and non-vanishing flux. Finally, we discuss magnetic p-form charges and electric/magnetic duality.

Dynamic Analysis and Hopf Bifurcation of a Lengyel–Epstein System with Two Delays

In this paper, a Lengyel–Epstein model with two delays is proposed and considered. By choosing the different delay as a parameter, the stability and Hopf bifurcation of the system under different situations are investigated in detail by using the linear stability method. Furthermore, the sufficient conditions for the stability of the equilibrium and the Hopf conditions are obtained. In addition, the explicit formula determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are obtained with the normal form theory and the center manifold theorem to delay differential equations. Some numerical examples and simulation results are also conducted at the end of this paper to validate the developed theories.

Stability and Hopf Bifurcation Analysis of a Reduced Gierer–Meinhardt Model

In this paper, we consider a reduction of the Gierer–Meinhardt Activator–Inhibitor model. In the absence of diffusion, we determine the global dynamics of the homogeneous system. Then, we study the effect of the diffusion constants on the stability of a homogeneous steady state. By choosing a proper bifurcation parameter, we prove that, under some suitable conditions on the parameters, a generalized Hopf bifurcation occurs in the inhomogeneos model. We compute the normal form of this bifurcation up to the fifth order. Furthermore, the direction of the Hopf bifurcation is obtained by the normal form theory. Finally, we provide some numerical simulations to justify our theoretical results.