scholarly journals Identifying nodal properties that are crucial for the dynamical robustness of multistable networks

2018 ◽  
Vol 98 (2) ◽  
Author(s):  
Pranay Deep Rungta ◽  
Chandrakala Meena ◽  
Sudeshna Sinha
Keyword(s):  
Nodal Properties

Unilateral Global Bifurcation from Infinity in Nonlinearizable One-Dimensional Dirac Problems

2021 ◽  
Vol 31 (01) ◽  
pp. 2150005
Author(s):  
Ziyatkhan S. Aliyev ◽  
Nazim A. Neymatov ◽  
Humay Sh. Rzayeva
Keyword(s):  
Dirac Equation ◽  
Eigenvalue Problems ◽  
Global Bifurcation ◽  
Nontrivial Solutions ◽  
One Dimensional ◽  
Bifurcation From Infinity ◽  
The One ◽  
Nodal Properties

In this paper, we study the unilateral global bifurcation from infinity in nonlinearizable eigenvalue problems for the one-dimensional Dirac equation. We show the existence of two families of unbounded continua of the set of nontrivial solutions emanating from asymptotically bifurcation intervals and having the usual nodal properties near these intervals.

scholarly journals Nodal solutions for the fractional Yamabe problem on Heisenberg groups

2019 ◽  
Vol 150 (2) ◽  
pp. 771-788 ◽  
Author(s):  
Alexandru Kristály
Keyword(s):  
Weak Solutions ◽  
Unitary Group ◽  
Original Problem ◽  
Laplacian Operator ◽  
Yamabe Problem ◽  
Heisenberg Groups ◽  
Nodal Solutions ◽  
Compactness Result ◽  
Homogeneous Dimension ◽  
Nodal Properties

AbstractWe prove that the fractional Yamabe equation ${\rm {\cal L}}_\gamma u = \vert u \vert ^{((4\gamma )/(Q-2\gamma ))}u$ on the Heisenberg group ℍn has [n + 1/2] sequences of nodal (sign-changing) weak solutions whose elements have mutually different nodal properties, where ${\rm {\cal L}}_\gamma $ denotes the CR fractional sub-Laplacian operator on ℍn, Q = 2n + 2 is the homogeneous dimension of ℍn, and $\gamma \in \bigcup\nolimits_{k = 1}^n [k,((kQ)/Q-1)))$. Our argument is variational, based on a Ding-type conformal pulling-back transformation of the original problem into a problem on the CR sphere S2n + 1 combined with a suitable Hebey-Vaugon-type compactness result and group-theoretical constructions for special subgroups of the unitary group U(n + 1).

Functional origin of rate-induced changes in atrioventricular nodal conduction time of premature beats in the rabbit

1987 ◽  
Vol 65 (11) ◽  
pp. 2329-2337 ◽  
Author(s):  
Jacques Billette ◽  
Marie St-Vincent
Keyword(s):  
Recovery Time ◽  
Rabbit Heart ◽  
Inhibitory Effect ◽  
Facilitatory Effect ◽  
Conduction Time ◽  
Recovery Times ◽  
Atrioventricular Nodal Conduction ◽  
Premature Beats ◽  
Induced Changes ◽  
Nodal Properties

The characteristics and origin of the rate-induced changes in atrioventricular nodal conduction time of premature beats (A2H2 intervals) were studied in isolated rabbit heart preparations. Increasing the basic driving rate during a periodic premature stimulation prolonged (a net inhibitory effect) and shortened (a net facilitatory effect) significantly (p < 0.01, n = 17) the A2H2 intervals associated with long and short recovery times (H1A2 intervals), respectively. The origin of these responses was sought for by analyzing interactions between facilitation and fatigue. When the fatigue developed at a fast basic rate was estimated from changes in conduction time of basic beats and subtracted from the corresponding A2H2 intervals, the calculated A2H2 intervals showed enhanced facilitation but no fatigue. When independently obtained fatigue and facilitation effects were added to the control A2H2 intervals for corresponding H1A2 intervals, resulting A2H2 intervals correlated strongly with the ones observed at the equivalent fast basic rate (r = 0.99, p < 0.001). Moreover, changes in the A2H2 intervals of premature beats tested with constant coupling intervals during 5-min fast rates were biphasic, confirming the overlapping and competition between facilitation and fatigue effects. Hence, rate-induced deviations of premature nodal conduction time from that predicted by changes in recovery time are consistent and result from the interaction between the overlapping effects produced by two independent, antagonist, and dynamically distinct nodal properties (facilitation and fatigue).

scholarly journals Existence of Sign-Changing Solutions to Equations Involving the One-Dimensional p-Laplacian

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Ruyun Ma ◽  
Lingfang Jiang
Keyword(s):  
Solutions To Equations ◽  
Quadrature Method ◽  
One Dimensional ◽  
The One ◽  
Sign Changing Solutions ◽  
Nodal Properties

We consider the equations involving the one-dimensional p-Laplacian (P):  (u′tp-2u′(t))′+λf(u(t))=0, 0<t<1, and u(0)=u(1)=0, where p>1,λ>0,f∈C1(R;R),f(s)s>0, and s≠0. We show the existence of sign-changing solutions under the assumptions f∞=lim|s|→∞⁡(fs/sp-1)=+∞ and f0=lim|s|→0(f(s)/sp-1)∈[0,∞]. We also show that (P) has exactly one solution having specified nodal properties for λ∈(0,λ*) for some λ*∈(0,∞). Our main results are based on quadrature method.

Multiplicity results for systems of asymptotically linear second order equations

2002 ◽  
Vol 2 (4) ◽  
Author(s):  
Anna Capietto ◽  
Francesca Dalbono
Keyword(s):  
Lower Bounds ◽  
Second Order ◽  
Upper And Lower Bounds ◽  
Asymptotically Linear ◽  
Multiplicity Results ◽  
Number Of Zeros ◽  
Existence And Multiplicity ◽  
Abstract Continuation Theorem ◽  
Nodal Properties ◽  
Second Order Equations

AbstractWe prove the existence and multiplicity of solutions, with prescribed nodal properties, for a BVP associated with a system of asymptotically linear second order equations. The applicability of an abstract continuation theorem is ensured by upper and lower bounds on the number of zeros of each component of a solution.

Subharmonic Solutions of Planar Hamiltonian Systems: a Rotation Number Approach

2011 ◽  
Vol 11 (1) ◽  
Author(s):  
Alberto Boscaggin
Keyword(s):  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Rotation Number ◽  
Subharmonic Solutions ◽  
Planar Hamiltonian System ◽  
Nodal Properties

AbstractWe prove the existence of infinitely many subharmonic solutions, with prescribed nodal properties, for a planar Hamiltonian system Jz′ = Δ

scholarly journals Global Bifurcation of Fourth-Order Nonlinear Eigenvalue Problems’ Solution

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Fatma Aydin Akgun
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fourth Order ◽  
Eigenvalue Problems ◽  
Global Bifurcation ◽  
Nonlinear Eigenvalue Problems ◽  
Nodal Properties ◽  
Nonlinear Eigenvalue

In this paper, we study the global bifurcation of infinity of a class of nonlinear eigenvalue problems for fourth-order ordinary differential equations with nondifferentiable nonlinearity. We prove the existence of two families of unbounded continuance of solutions bifurcating at infinity and corresponding to the usual nodal properties near bifurcation intervals.

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