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المادية المقاتلة : رد على السيد بوجدانوف
بلیخانوف هو المؤسس الحقيقي للماركسية في روسيا، ولد عام 1857 وشكل عام 1883 في جنيف فرقة تحرير العمل، لعبت مؤلفات بلیخانوف دورا كبيرا في نشر الماركسية، ولعب دورا هاما في تكوين شخصية لينين الذي كان أصغر منه بكثير. حدث انقسام داخل الحزب الاشتراكي الديمقراطي بين البلشفيك بقيادة لينين، والمنشفيك، فوقف بلیخانوف مترددا بين الفئتين، إلى أن انضم في النهاية إلى المونشفيك. ووقعت القطيعة نهائيا بينه وبين لينين، ولما نشبت الثورة البولشفية عام 1917 عاد إلى روسيا ولكنه رفض الاشتراك في الحكم وظل ضد البلشفية حتى مات بفنلندا عام 1918. كتب لينين عام 1921 فيما يتعلق بكتابات بليخانوف (أظن أنه من اللائق أن أبدي ملاحظة لمصلحة أعضاء الحزب الشباب، تلكم هي أنك في أي مكان من العالم، أحسن من هذه الدراسات). لقد كان نضال بليخانوف ضد المذهب الماخي والفوضوية وأنواع أخرى من المثالية، حدثا هاما في تاريخ الفلسفة الماركسية. وقد وجهت الرسائل الثلاث التي يتكون منها كتاب (المادية المقاتلة) بصورة أساسية ضد بوجدانوف (وهو فيلسوف وعالم اجتماع واقتصادي) الممثل البارز للماخية الروسية.
BOOK
Red Hamlet : the life and ideas of Alexander Bogdanov
In this first full-length biography, James D. White traces Alexander Bogdanov's intellectual development, examining his role in the evolution of Marxist thought in Russia, and his place in the Russian revolutionary movement.
eBook
Bifurcations in planar, quadratic mass-action networks with few reactions and low molecularity
In this paper we study bifurcations in mass-action networks with two chemical species and reactant complexes of molecularity no more than two. We refer to these as planar, quadratic networks as they give rise to (at most) quadratic differential equations on the nonnegative quadrant of the plane. Our aim is to study bifurcations in networks in this class with the fewest possible reactions, and the lowest possible product molecularity. We fully characterise generic bifurcations of positive equilibria in such networks with up to four reactions, and product molecularity no higher than three. In these networks we find fold, Andronov–Hopf, Bogdanov–Takens and Bautin bifurcations, and prove the non-occurrence of any other generic bifurcations of positive equilibria. In addition, we present a number of results which go beyond planar, quadratic networks. For example, we show that mass-action networks without conservation laws admit no bifurcations of codimension greater than
m
-
2
, where
m
is the number of reactions; we fully characterise quadratic, rank-one mass-action networks admitting fold bifurcations; and we write down some necessary conditions for Andronov–Hopf and cusp bifurcations in mass-action networks. Finally, we draw connections with a number of previous results in the literature on nontrivial dynamics, bifurcations, and inheritance in mass-action networks.
Journal Article
Bifurcation analysis in a predator–prey system with a functional response increasing in both predator and prey densities
This paper presents a qualitative study of a predator–prey interaction system with the functional response proposed by Cosner et al. (Theor Popul Biol 56:65–75,
1999
). The response describes a behavioral mechanism which a group of predators foraging in linear formation searches, contacts and then hunts a school of prey. On account of the response, strong Allee effects are induced in predators. In the system, we determine the existence of all feasible nonnegative equilibria; further, we investigate the stabilities and types of the equilibria. We observe the bistability and paradoxical phenomena induced by the behavior of a parameter. Moreover, we mathematically prove that the saddle-node, Hopf and Bogdanov–Takens types of bifurcations can take place at some positive equilibrium. We also provide numerical simulations to support the obtained results.
Journal Article
Complex dynamics of a predator-prey model with opportunistic predator and weak Allee effect in prey
In this work, we first modify a Lotka-Volterra predator-prey system to incorporate an opportunistic predator and weak Allee effect in prey. The prey will be extinct if the combined effect of hunting and other food resources of predator is large. Otherwise, the dynamic behaviour of the system is extremely rich. A series of bifurcations such as saddle-node bifurcation, Hopf bifurcation, and Bogdanov-Takens bifurcation can happen. The validity of the theoretical results are supported with numerical simulations.
Journal Article
Bogdanov–Takens bifurcation of an enzyme-catalyzed reaction model
Enzyme-catalyzed reactions are frequently observed in the chemical process, and could be described by the mathematical model, such as the Gray–Scott model with Langmuir–Hinshelwood mechanism. The complex dynamical behaviors are analyzed in this work, including the existence and their stability of equilibrium points and the bifurcations of the model. By using stability theory, normal form technique and bifurcation analysis, the stability and the saddle-node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation are explored in detail. Numerical simulations are also carried out to verify the validity of theoretical results.
Journal Article
An SIRS model with nonmonotone incidence and saturated treatment in a changing environment
Nonmonotone incidence and saturated treatment are incorporated into an SIRS model under constant and changing environments. The nonmonotone incidence rate describes the psychological or inhibitory effect: when the number of the infected individuals exceeds a certain level, the infection function decreases. The saturated treatment function describes the effect of infected individuals being delayed for treatment due to the limitation of medical resources. In a constant environment, the model undergoes a sequence of bifurcations including backward bifurcation, degenerate Bogdanov-Takens bifurcation of codimension 3, degenerate Hopf bifurcation as the parameters vary, and the model exhibits rich dynamics such as bistability, tristability, multiple periodic orbits, and homoclinic orbits. Moreover, we provide some sufficient conditions to guarantee the global asymptotical stability of the disease-free equilibrium or the unique positive equilibrium. Our results indicate that there exist three critical values r1,r2 and r3 for the treatment rate r: (i) when r≥max{r1,r2}, the disease will disappear; (ii) when r1 predicts regime shifts that cause the delayed disease outbreak in a changing environment. Furthermore, the disease can disappear in advance (or belatedly) if the rate of environmental change is negative and large (or small). The transient dynamics of an infectious disease heavily depend on the initial infection number and rate or the speed of environmental change.
Journal Article
Bogdanov–Takens bifurcation analysis of a delayed predator-prey system with double Allee effect
The Bogdanov–Takens (B–T) bifurcation of a delayed predator-prey system with double Allee effect in prey are studied in this paper. According to the existence conditions of B–T bifurcation, we give the associated generic unfolding, and derive the normal forms of the B–T bifurcation of the model at its interior equilibria by generalizing and using the normal form theory and center manifold theorem for delay differential equations. By analyzing the topologically equivalent normal form system, one find that the Allee effect and delay can lead to varies dynamic behaviors, which is believed to be beneficial for understanding the potential mathematical mechanism that driving population dynamics.
Journal Article
Dynamic Interplay: Cooperative Hunting Strategies in a Predator-Prey Model with Smith Growth Dynamics
In this research paper, we delve into the critical examination of interactions between predators and prey within ecological systems. Drawing on principles from theoretical biology and mathematical ecology, our study introduces a predator-prey model that incorporates the Smith growth rate of prey and Holling type II functional response, while uniquely considering the influence of hunting cooperation between predators. We rigorously explore various aspects such as positivity, boundedness, local stability, and different bifurcation types, including transcritical, saddle-node, Hopf, cusp, and Bogdanov-Takens bifurcation. Both theoretical analyses and graphical representations are employed to offer a comprehensive understanding of the system dynamics. To unravel the complexity of the interactions, we present two-parametric bifurcation diagrams, utilizing
a
and
K
as bifurcation parameters. The first quadrant of the
a
-
K
plane is systematically partitioned into seven regions, demarcated by distinct bifurcation curves. Bistable dynamics are exhibited in the ecological system. A notable observation stemming from our investigation is the vulnerability of the predator population to extinction at low carrying capacity values. Furthermore, our numerical findings underscore the enhanced stability of the system with an increase in hunting cooperation. This research contributes valuable insights into the intricate dynamics of predator-prey interactions, shedding light on the significance of ecological parameters and cooperative behaviors in shaping the stability and persistence of these systems.
Journal Article