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In the paper, we consider a nonlinear integrodifferential equation of the third order with delay. We establish sufficient conditions guaranteeing the global existence and boundedness of the solutions of the analyzed equation. We use the Lyapunov second method to prove the main result. An example is also given to illustrate the applicability of our result. The result of this paper is new and improves previously known results. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the dynamics of a predator-prey model with Beddington-DeAngelis functional response and nonselective harvesting. By using the Lyapunov-Schmidt reduction, we obtain the existence of spatially nonhomogeneous steady-state solution. The stability and existence of Hopf bifurcation at the spatially nonhomogeneous steady-state solution with the change of a specific parameter are investigated by analyzing the distribution of the eigenvalues. We also get an algorithm for determining the bifurcation direction of the Hopf bifurcating periodic solutions near the nonhomogeneous steady-state solution. Finally, we show some numerical simulations to verify our analytical results. [ABSTRACT FROM AUTHOR]

In this paper we define the index at infinity of an asymptotically linear autonomous Hamiltonian system. We use this index to prove the existence and bifurcation from infinity of periodic solutions of the system. We apply the degree for G-invariant strongly indefinite functionals defined by Gołȩbiewska and Rybicki in (Nonlinear Anal 74:1823-1834, 2011). [ABSTRACT FROM AUTHOR]

In this paper, a comprehensive analysis is presented to investigate a codimension two bifurcation that exists in a nonlinear railway bogie dynamic system combining theoretical analysis with numerical investigation. By using the running velocity V and the primary longitudinal stiffness K1x as bifurcation parameters the first and second Lyapunov coefficients are calculated to determine which kind of Hopf bifurcation can happen and how the system states change with the variance of the bifurcation parameters. It is found that multiple solution branches both stable and unstable coexist in a range of the bifurcation parameters which can lead to jumps in the lateral oscillation amplitude of the railway bogie system. Furthermore, reduce the values of the bifurcation parameters gradually. Firstly, the supercritical Hopf bifurcation turns into a subcritical one with multiple limit cycles both stable and unstable near the Hopf bifurcation point. With a further reduction in the bifurcation parameters two saddle-node bifurcation points emerge, resulting in the loss of the stable limit cycle between these two bifurcation points. [ABSTRACT FROM AUTHOR]

In this paper bifurcations of heterodimensional cycles with highly degenerate conditions are studied in three dimensional vector fields, where a nontransversal intersection between the two-dimensional manifolds of the saddle equilibria occurs. By setting up local moving frame systems in some tubular neighborhood of unperturbed heterodimensional cycles, the authors construct a Poincaré return map under the nongeneric conditions and further obtain the bifurcation equations. By means of the bifurcation equations, the authors show that different bifurcation surfaces exhibit variety and complexity of the bifurcation of degenerate heterodimensional cycles. Moreover, an example is given to show the existence of a nontransversal heterodimensional cycle with one orbit flip in three dimensional system. [ABSTRACT FROM AUTHOR]

In this paper, we present a numerical study of the pulsatile transitional flow crossing a severe real stenosis located right in front of the bifurcation between the right subclavian and right common carotid arteries. The simulation allows one to determine relevant features of this subject-specific flow, such as the pressure waves in the right subclavian and right common carotid arteries. We explain the subclavian steal syndrome suffered by the patient in terms of the drastic pressure drop in the right subclavian artery. This pressure drop is caused by both the diverging part of the analyzed stenosis and the reverse flow in the bifurcation induced by another stenosis in the right internal carotid artery. [ABSTRACT FROM AUTHOR]

Vibrational behavior of harmonically excited MDOF oscillators subjected to multiple contact constraints is investigated in this paper using the combination of the Newmark integration scheme and the Linear complementarity problem (LCP) formulation. An oscillator with gap-activated non-smooth spring constraints exhibits various complex behavior such as sub-harmonic resonances, bifurcations and chaos, which are effectively predicted using the proposed method. Numerical results were obtained and presented for SDOF and 5-DOF systems with frequency and stiffness parameters varying in wide ranges to validate the Newmark-LCP method and to demonstrate its effectiveness in dealing with MDOF systems with multiple contact constraints. [ABSTRACT FROM AUTHOR]

In this paper, we present computational techniques to investigate the effect of surface geometry on biological pattern formation. In particular, we study two-component, nonlinear reaction-diffusion (RD) systems on arbitrary surfaces. We build on standard techniques for linear and nonlinear analysis of RD systems and extend them to operate on large-scale meshes for arbitrary surfaces. In particular, we use spectral techniques for a linear stability analysis to characterise and directly compose patterns emerging from homogeneities. We develop an implementation using surface finite element methods and a numerical eigenanalysis of the Laplace-Beltrami operator on surface meshes. In addition, we describe a technique to explore solutions of the nonlinear RD equations using numerical continuation. Here, we present a multiresolution approach that allows us to trace solution branches of the nonlinear equations efficiently even for large-scale meshes. Finally, we demonstrate the working of our framework for two RD systems with applications in biological pattern formation: a Brusselator model that has been used to model pattern development on growing plant tips, and a chemotactic model for the formation of skin pigmentation patterns. While these models have been used previously on simple geometries, our framework allows us to study the impact of arbitrary geometries on emerging patterns. [ABSTRACT FROM AUTHOR]

The paper studies a codimension-4 resonant homoclinic bifurcation with one orbit flip and two inclination flips, where the resonance takes place in the tangent direction of homoclinic orbit. Local active coordinate system is introduced to construct the Poincaré returning map, and also the associated successor functions. We prove the existence of the saddle-node bifurcation, the period-doubling bifurcation and the homoclinic-doubling bifurcation, and also locate the corresponding 1-periodic orbit, 1-homoclinic orbit, double periodic orbits and some 2-homoclinic orbits. [ABSTRACT FROM AUTHOR]

A complete description of the real phase topology of a two fixed center problem is introduced and studied. Moreover, all generic bifurcations of Liouville tori are determined theoretically and the periodic solution is presented. At the end of this paper, the phase portrait is studied. [ABSTRACT FROM AUTHOR]