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Global Stability Analysis of Healthy Situation for a Coupled Model of Healthy and Cancerous Cells Dynamics in Acute Myeloid Leukemia
In this paper we aim to study the global stability of a coupled model of healthy and cancerous cells dynamics in healthy situation of Acute Myeloid Leukemia. We also clarify the effect of interconnection between healthy and cancerous cells dynamics on the global stability The interconnected model is obtained by transforming the PDE-based model into a nonlinear distributed delay system. Using Lyapunov approach, we derive necessary and sufficient conditions for global stability for a selected equilibrium point of particular interest (healthy situation). Simulations are conducted to illustrate the obtained results
Sum-of-squares of polynomials approach to nonlinear stability of fluid flows: an example of application
With the goal of providing the first example of application of a recently proposed method, thus demonstrating its ability to give results in principle, global stability of a version of the rotating Couette flow is examined. The flow depends on the Reynolds number and a parameter characterising the magnitude of the Coriolis force. By converting the original Navier-Stokes equations to a finite-dimensional uncertain dynamical system using a partial Galerkin expansion, high-degree polynomial Lyapunov functionals were found by sum-of-squares-of-polynomials optimization. It is demonstrated that the proposed method allows obtaining the exact global stability limit for this flow in a range of values of the parameter characterising the Coriolis force. Outside this range a lower bound for the global stability limit was obtained, which is still better than the energy stability limit. In the course of the study several results meaningful in the context of the method used were also obtained. Overall, the results obtained demonstrate the applicability of the recently proposed approach to global stability of the fluid flows. To the best of our knowledge, it is the first case in which global stability of a fluid flow has been proved by a generic method for the value of a Reynolds number greater than that which could be achieved with the energy stability approach
Global Stability Conditions on the Plane
The paper considers price adjustment on the plane and derives global stability conditions for such dynamics. First, we examine the well-known Scarf Example, to obtain and analyze a global stability condition for this case. Next, for a general class of excess demand functions, a set of conditions is identified which guarantee not only convergence to some equilibrium but also robustness of these properties.
The global stability of M33: still a puzzle
The inner disc of the local group galaxy M33 appears to be in settled
rotational balance, and near IR images reveal a mild, large-scale, two-arm
spiral pattern with no strong bar. We have constructed N-body models that match
all the extensive observational data on the kinematics and surface density of
stars and gas in the inner part of M33. We find that currently favoured models
are unstable to the formation of a strong bar of semi-major axis 2 < a_B < 3
kpc within 1 Gyr, which changes the dynamical properties of the models to
become inconsistent with the current, apparently well-settled, state. The
formation of a bar is unaffected by how the gas component is modelled, by
increasing the mass of the nuclear star cluster, or by making the dark matter
halo counter-rotate, but it can be prevented by either reducing the
mass-to-light ratio of the stars to Upsilon_V ~ 0.6 or Upsilon_K ~ 0.23 in
solar units or by increasing the random motions of the stars. Also a shorter
and weaker bar results when the halo is rigid and unresponsive. However, all
three near-stable models support multi-arm spirals, and not the observed
large-scale bi-symmetric spiral. A two-arm spiral pattern could perhaps be
tidally induced, but such a model would require an implausibly low mass disc to
avoid a bar and there is no visible culprit. Thus the survival of the current
state of this exceptionally well-studied galaxy is not yet understood. We also
suspect that many other unbarred galaxies present a similar puzzle.Comment: 15 pages, 8 figures, to appear in MNRAS. A nymber of revisions from
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Global stability and repulsion in autonomous Kolmogorov systems
Criteria are established for the global attraction, or global repulsion on a compact invariant set, of interior and boundary fixed points of Kolmogorov systems. In particular, the notions of diagonal stability and Split Lyapunov stability that have found wide success for Lotka-Volterra systems are extended for Kolmogorov systems. Several examples from theoretical ecology and evolutionary game theory are discussed to illustrate the results
Restrictions and Stability of Time-Delayed Dynamical Networks
This paper deals with the global stability of time-delayed dynamical
networks. We show that for a time-delayed dynamical network with
non-distributed delays the network and the corresponding non-delayed network
are both either globally stable or unstable. We demonstrate that this may not
be the case if the network's delays are distributed. The main tool in our
analysis is a new procedure of dynamical network restrictions. This procedure
is useful in that it allows for improved estimates of a dynamical network's
global stability. Moreover, it is a computationally simpler and much more
effective means of analyzing the stability of dynamical networks than the
procedure of isospectral network expansions introduced in [Isospectral graph
transformations, spectral equivalence, and global stability of dynamical
networks. Nonlinearity, 25 (2012) 211-254]. The effectiveness of our approach
is illustrated by applications to various classes of Cohen-Grossberg neural
networks.Comment: 32 pages, 9 figure
Landscape and flux for quantifying global stability and dynamics of game theory
Game theory has been widely applied to many areas including economics,
biology and social sciences. However, it is still challenging to quantify the
global stability and global dynamics of the game theory. We developed a
landscape and flux framework to quantify the global stability and global
dynamics of the game theory. As an example, we investigated the models of
three-strategy games: a special replicator-mutator game, the repeated prison
dilemma model. In this model, one stable state, two stable states and limit
cycle can emerge under different parameters. The repeated Prisoner's Dilemma
system has Hopf bifurcation transitions from one stable state to limit cycle
state, and then to another one stable state or two stable states, or vice
versa. We explored the global stability of the repeated Prisoner's Dilemma
system and the kinetic paths between the basins of attractor. The paths are
irreversible due to the non-zero flux. One can explain the game for and
.Comment: 25 pages, 15 figure
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