The application of mathematics, physics and engineering to medical research is continuously growing; interactions among these disciplines have become increasingly important and have contributed to an improved understanding of clinical and biological phenomena, with implications for disease prevention, diagnosis and treatment. This special issue presents examples of this synergy, with a particular focus

In this paper, we develop an unconditionally stable linear numerical scheme for the N-component Cahn–Hilliard system with second-order accuracy in time and space. The proposed scheme is modified from the Crank–Nicolson finite difference scheme and adopts the idea of a stabilized method. Nonlinear multigird algorithm with Gauss–Seidel-type iteration is used to solve the resulting discrete system. We

In this work, we consider a partial differential equation that extends the well-known Fermi–Pasta–Ulam–Tsingou chains from nonlinear dynamics. The continuous model under consideration includes the presence of both a damping term and a polynomial function in terms of Riesz space-fractional derivatives. Initial and boundary conditions on a closed and bounded interval are considered in this work. The

We consider a modification of the well studied Hamiltonian Mean-Field model with cosine potential by introducing a hard-core point-like repulsive interaction and propose a numerical integration scheme to integrate its dynamics. Our results show that the outcome of the initial violent relaxation is altered, and also that the phase-diagram is modified with a critical temperature at a higher value than

In this paper a stability analysis for a Cournot duopoly model with tax evasion and time-delay in a continuous-time framework is presented. The mathematical model under consideration follows a gradient dynamics approach, is nonlinear and four-dimensional with state variables given by the production and declared revenue of each competitor. We prove that both the marginal cost rate and time delay play

The cylindrical Kadomtsev-Petviashvili (cKP) equation related to cylindrical geometry, as one type of the variable-coefficient KP equation, is widely used to describe nonlinear phenomena in fluid, plasma and other fields. With symbolic computation, we have derived the multi-soliton solutions, rational solutions, lump solutions and interaction solutions to the cKP equation based on its bilinear representation

Recently, many algorithms have emerged inspired by the biological behavior of animal life to deal with complicated applications such as combinatorial optimization. One of the most critical discussions involving these algorithms is concerning their objective functions. Also, recently, many works have demonstrated the efficiency of Tsallis non-extensive statistics in several applications. However, this

This paper proposes and analyzes a viral infection model that characterizes the interactions of the viruses, susceptible host cells, n-stages of infected cells, B cells and CTL cells. We consider both virus-to-cell and cell-to-cell transmissions and n+1 intracellular distributed time delays. The incidence rate of infection as well as the generation and removal rates of all compartments are described

By using both a phase field approach and a modified level set approach, two multiphase numerical models are proposed and compared in this paper to investigate the ferrodroplet deformation and merging process in a non-magnetic viscous medium under the influence of uniform magnetic fields. The finite element method is utilized for the spatial discretization of both numerical models. The numerical results

We introduce a nonlinear Schrödinger equation (NLSE) which combines the pseudo-stimulated-Raman-scattering (pseudo-SRS) term, i.e., a non-conservative cubic one with the first spatial derivative, and an external potential, which helps to stabilize solitons against the pseudo-SRS effect. Dynamics of solitons is addressed by means of analytical and numerical methods. The quasi-particle approximation

We analyze the diffusion of a system on a backbone structure, by considering the presence of reaction terms. We start our analysis by considering an irreversible reaction process, where the particles are removed from the system. After, we consider the diffusion subjected to a reversible reaction process. The behavior for the system in this scenario depends on the relative rates of diffusion and reaction

In this paper, we investigate the European option pricing problem under a regime switching FMLS (finite moment log-stable) model. This model is not only able to capture the main characteristics of asset returns, it also incorporates the effect of regime switching being consistent with market observations. However, option prices under this model are governed by a coupled FPDE (fractional partial differential

Bose-Einstein condensates (BECs) provide a clear and controllable platform to study diverse intriguing emergent nonlinear effects that appear too in other physical settings, such as bright and dark solitons in mean-field theory as well as many-body physics. Various ways have been elaborated to stabilize bright solitons in BECs, three promising schemes among which are: optical lattices formed by counterpropagating

In order to explore the impacts of the time-delayed velocity difference and backward looking effect on traffic flow, this paper proposes an improved car-following model based on the full velocity difference model (FVDM) by accounting for the time-delayed velocity difference and backward looking effect. The linear stability condition of the proposed model is derived by taking advantage of the linear

There are several theoretically well-posed models for the Allen–Cahn equation under mass conservation. The conservative property is a gift from the additional nonlocal term playing a role of a Lagrange multiplier. However, the same term destroys the boundedness property that the original Allen–Cahn equation presents: The solution is bounded by 1 with an initial datum bounded by 1. In this paper, we

This paper extends and improves the Newton algorithm to solve contact and wear problems with pressure-dependent friction coefficients. Especially, the wear problems with pressure-dependent friction coefficients are numerically solved for the first time. The contact forces are calculated by the bipotential method. Combining the calculation steps of contact forces with the local equilibrium equations

Analytic solutions in implicit form are derived for a nonlinear partial differential equation (PDE) with fractional derivative elements, which can model the dynamics of a deterministically excited Euler-Bernoulli beam resting on a viscoelastic foundation. Specifically, the initial-boundary value problem for the corresponding PDE is reduced to an initial value problem for a nonlinear ordinary differential

We introduce a new general class of nonlinear variable order fractional partial differential equations (NVOFPDE). The NVOFPDE contains, as special cases, several partial differential equations, such as the nonlinear variable order (VO) fractional equations usually denoted as Klein-Gordon, diffusion-wave and convection-diffusion-wave. To find the numerical solution of the NVOFPDE, we formulate a novel

We make a detailed numerical study of a three dimensional dissipative vector field derived from the normal form for a cusp-Hopf bifurcation. The vector field exhibits a Neimark–Sacker bifurcation giving rise to an attracting invariant torus. Our main goals are to (A) follow the torus via parameter continuation from its appearance to its disappearance, studying its dynamics between these events, and

A new type of spiral wave caused by the pitchfork bifurcation of a limit cycle is reported, which may exist in ecosystems containing two (or more) species that are not symbiotic. The dynamical behavior of the spiral wave is explained by a superposition principle of disturbance intensity vectors in oscillatory media. This type of spiral wave is characterized by a slow-moving line-defect that passes

We study scaling features in the reactions of cereral blood vessel network to sudden “jumps” in peripheral arterial pressure in rats. Using laser speckle contrast imaging (LSCI) to measure the relative velocity of cerebral blood flow (CBF) and detrended fluctuation analysis (DFA) for processing experimental data, we investigate distinctions in the responses of veins and capillaries. To quantify short-term

In this paper we study the phenomena of the extinction and persistence of predator populations of the three-dimensional Kooi et al. model in the global formulation of the problem. This model contains three populations: prey, susceptible predators and infected predators. We compute ultimate sizes of interacting populations and establish that all biologically feasible trajectories eventually enter in

Lasota and Myjak demonstrated that one can study attractors to an iterated function system (IFS) possibly containing discontinuous functions. We continue this line of thought by working with IFS with a lower semicontinuous Hutchinson-Barnsley operator and two new (but not significantly different) types of attractors, the small attractor (the smallest closed nonempty invariant set) and minimal attractors

The reported efficacy of biofeedback is not consistent across studies. One issue that has not been addressed in previous studies is the effect of the reference signal in a biofeedback system. We compared the effects of two different reference signals using a computational model and human experiments. One reference signal was fixed, and the other was variable and was designed based on time-delayed feedback

Van der Pol and Rayleigh oscillators are two traditional paradigms of nonlinear dynamics. They can be subsumed into a general form of Liénard–Levinson–Smith(LLS) system. Based on a recipe for finding out maximum number of limit cycles possible for a class of LLS oscillator, we propose here a scheme for systematic designing of generalised Rayleigh and Van der Pol families of oscillators with a desired

This work proposes the numerical solutions of the cubic nonlinear Schrödinger equation subjected to rational initial value for three cases, (i) Akhmediev breather (ii) Peregrine and (iii) Kuznetsov-Ma solitons by operating exponential time differencing method (ETDM). The work shows that ETDM is a reliable and accurate method to find the solutions comparing to Adomian decomposition method (ADM) and

The lumped mass model is derived from a one-mode Galerkin discretization with the Gauss–Lobatto quadrature applied to the non-linear swelling pressure term. Our reduced-order model of the problem is then analyzed to study the essential dynamics of an elastic cantilever Euler–Bernoulli beam subject to the swelling pressure described by Grob’s law. The solutions to the initial value problem for the resulting

Co-infections by multiple pathogens have important implications in many aspects of health, epidemiology and evolution. However, how to disentangle the non-linear dynamics of the immune response when two infections take place at the same time is largely unexplored. Using data sets of the immune response during influenza-pneumococcal co-infection in mice, we employ here topological data analysis to simplify

Individuals often form their identity based on their membership in a group and may exhibit a bias towards favoring members of the in-group (Greenwald and Pettigrew, 2014). When resources are plentiful, individuals are more likely to be tolerant of members of out-group sharing the resources. However, when there is a scarcity of resources, the resource stress could lead to a negative attitude towards

In artificial neural networks, the diffusion phenomenon of electrons exists inevitably, due to the electromagnetic field of neural networks is heterogeneous. In this paper, we study the spatio-temporal dynamical behaviors of a reaction-diffusion neural network with leakage delay. By analyzing the corresponding characteristic equation, the sufficient and necessary conditions of Turing instability are

In this paper, finite-time synchronization issue of fractional-order complex-valued dynamical networks with multiple weights is addressed. Multiple weights are pulled into consideration, which makes our model more practical and general than single-weight one. Combining Lyapunov method with graph-theoretic method and making use of the theory of complex functions, finite-time synchronization criteria

This paper attempts to investigate the stochastic resonance (SR) phenomenon in a delay-controlled dissipative bistable potential with time-delayed feedback under the action of harmonic excitation and additive noise by using small delay approximation theory and signal-to-noise ratio (SNR) theory. The time delay and feedback strength are able to adjust the potential shapes precisely by fusing potential

Four novel implicit finite difference methods with (q+s)-th order in space based on (q, s)-Padé approximations have been analyzed and developed for the sine-Gordon equation. Specifically, (4,0)-, (2,2)-, (4,2)-, and (4,4)-Padé methods. All of them share the treatment for the nonlinearity and integration in time, specifically, the one that results in an energy-conserving (2,0)-Padé scheme. The five

The purpose of this paper is to examine a special kind of game option, whose main feature is the presence of an early exercise right for the seller as well as for the buyer. The seller has to pay some amount above the usual option payment for this right. Usually, this penalty payment is presented by a constant amount during the option life. Alternatively, in this paper we present the cancellation payment

In this paper the scattering between the non-topological kinks arising in a family of two-component scalar field theory models is analyzed. A winding charge is carried by these defects. As a consequence, two different classes of kink scattering processes emerge: (1) collisions between kinks that carry the same winding number and (2) scattering events between kinks with opposite winding number. The

We study coupled unstaggered-staggered soliton pairs emergent from a system of two coupled discrete nonlinear Schrödinger (DNLS) equations with the self-attractive on-site self-phase-modulation nonlinearity, coupled by the repulsive cross-phase-modulation interaction, on 1D and 2D lattice domains. These mixed modes are of a “symbiotic” type, as each component in isolation may only carry ordinary unstaggered

The Rate Control Protocol (RCP) uses explicit feedback from routers to control network congestion. RCP estimates it’s fair rate from two forms of feedback: rate mismatch and queue size. An important design question that remains open in RCP is whether the presence of queue size feedback is helpful, given the presence of feedback from rate mismatch. The feedback from routers to end-systems is time-delayed

We show that the integrable equations of hydrodynamic type admit nonlocal reductions. We first construct such reductions for a general Lax equation and then give several examples. The reduced nonlocal equations are of hydrodynamic type and integrable. They admit Lax representations and hence possess infinitely many conserved quantities.

This paper deals with the planar three-body problem with equal masses and moving under 1/r2 potential. The complete reduction of this problem is done by using its finite group of symmetries and the Jacobi-Maupertuis metric. We show that it is the unfolding of a flow which is topologically conjugate to a geodesic billiard problem with the Jacobi-Maupertuis metric. Finally there is a numerical exploration

We investigate a possibility to describe the non-Debye relaxation processes using the Volterra-type equations with kernels given by the Prabhakar functions with the upper parameter ν being negative. Proposed integro-differential equations mimic the fading memory effects and are explicitly solved using the umbral calculus and the Laplace transform methods. Both approaches lead to the same results valid

Excitatory autapse with short time delay can lower the firing frequency of spiking behaviors near subcritical Hopf bifurcation, which is interpreted with type II phase response curve wherein an excitatory impulse current applied at the phase following a spike can induce the next spike delayed. Such a nonlinear phenomenon is different from the common viewpoint that excitatory effect typically induces

Based on the time-frequency analysis, a piecewise re-scaled method is proposed to realize aperiodic resonance in a Duffing system excited by the nonlinear frequency modulated (NLFM) signal. Based on the aperiodic resonance theory, the weak NLFM signal is enhanced greatly. By short time Fourier transform, numerical simulations are carried out for several kinds of NLFM signal. The results show that the

In cardiac myocytes, calcium cycling links the dynamics of the membrane potential to the activation of the contractile filaments. Perturbations of the calcium signalling toolkit have been demonstrated to disrupt this connection and lead to numerous pathologies including cardiac alternans. This rhythm disturbance is characterised by alternations in the membrane potential and the intracellular calcium

This study examines the problem of impulsive and pinning control synchronization of Markovian jumping master-slave complex dynamical networks with hybrid coupling and additive interval time-varying delays. The linear couplings include both the discrete time-varying delay and the distributed time-varying delays. Two kinds of control schemes are utilized to synchronize the considered dynamical network

In this paper, modified Zakharov-Kuznetsov (mZK) equation is taken into consideration. Diverse variety of solitonic structures are computed by using extended algebraic method. Sufficient conditions for the existence of the computed solutions are presented. Then, Galilean transformation is utilized to transform the considered model in the planer dynamical system. All possible forms of phase portraits

This work presents new adaptive time-step schemes based on the Uniformization method for solving stiff electrophysiology models of excitable cells. Uniformization is a numerical method for continuous-time Markov chains that was proven to be effective in solving modern membrane models that have ion channels described by Markov chains. The new methods were tested using three highly stiff cell models

This paper proposes the concept of Razumikhin-type functional differential inequalities and points out that certain quantitative properties can be established for the Razumikhin-type functional differential inequalities. By virtue of certain auxiliary functions, some fundamental results on the quantitative bounds for the Razumikhin-type functional differential inequalities are systemically established

Recently, a novel bifurcation technique known as deflated continuation was applied to the single-component nonlinear Schrödinger (NLS) equation with a parabolic trap in two spatial dimensions. This bifurcation analysis revealed previously unknown solutions, shedding light on this fundamental problem in the physics of ultracold atoms. In the present work, we take this a step further by applying deflated

The dynamics of solar-sail maneuvers is conceptually different from classical control maneuvers where one considers impulsive changes in the velocity of a spacecraft. Solar-sail orbits are continuous in both position and velocity in a varying vectorfield, opening the possibility of the existence of heteroclinic connections by means of artificially changing the vectorfield with a sail maneuver. This

Hierarchical code coupling strategies make it possible to combine the results of individual numerical solvers into a self-consistent symplectic solution. We explore the possibility of allowing such a coupling strategy to be non-intrusive. In that case, the underlying numerical implementation is not affected by the coupling itself, but its functionality is carried over in the interface. This method

In this work we revisit a classical problem of traveling waves in a damped Frenkel-Kontorova lattice driven by a constant external force. We compute these solutions as fixed points of a nonlinear map and obtain the corresponding kinetic relation between the driving force and the velocity of the wave for different values of the damping coefficient. We show that the kinetic curve can become non-monotone

This paper explores the internal dynamical mechanisms of epileptic seizures through quantitative modeling based on full brain electroencephalogram (EEG) signals. Our goal is to provide seizure prediction and facilitate treatment for epileptic patients. Motivated by an earlier mathematical model with incorporated synaptic plasticity, we studied the nonlinear dynamics of inherited seizures through a

The paper introduces a matrix-based approach to estimate the unique one-dimensional discrete-time dynamical system that generated a given sequence of probability density functions whilst subjected to an additive stochastic perturbation with known density.

This paper presents a very effective numerical method for the solution of the two-compartmental pharmacokinetic model for oral drug administration. This model consists of a set of two fractional order differential equations which connect the two compartments. The first compartment represents the gut while the second compartment corresponds to the drug concentration in the target tissue. For ease of

We report the appearance of anomalous water diffusion in hydrophilic Sephadex gels observed using pulse field gradient (PFG) nuclear magnetic resonance (NMR). The NMR diffusion data was collected using a Varian 14.1 Tesla imaging system with a home-built RF saddle coil. A fractional order analysis of the data was used to characterize heterogeneity in the gels for the dynamics of water diffusion in