In the absence of inhibition, excitatory neuronal networks can alternate between bursts and interburst intervals (IBI), with heterogeneous length distributions. As this dynamic remains unclear, especially the durations of each epoch, we develop here a bursting model based on synaptic depression and facilitation that also accounts for afterhyperpolarization (AHP), which is a key component of IBI. The

The structure of complex oscillations with two time scales generated by a novel memristor-based Shinriki’s circuit is studied in detail. Employing the stability phase diagrams, we identify the parameter regions of mixed-mode oscillations (MMOs) produced by each state variable, and classify the fast and slow properties of state variables according to the characteristics of these MMOs. Additionally,

In the paper, we study approximation properties of the Malmquist-Takenaka-Christov (MTC) system. We show that the discrete MTC approximations converge rapidly under mild restrictions on functions asymptotic at infinity. This makes them particularly suitable for solving semi- and quasi-linear problems containing Fourier multipliers, whose symbols are not smooth at the origin. As a concrete application

Coupled oscillators exhibit intriguing dynamical states characterized by the coexistence of coherent and incoherent domains known as chimera states. Similar behaviors have been observed in coupled systems and continuous media. Here we investigate the transition from motionless to traveling chimera states in continuous media. Based on a prototype model for pattern formation, we observe coexistence between

Fractal geometry is one of the beautiful and challenging branches of mathematics. Self similarity is an important property, exhibited by most of the fractals. Several forms of self similarity have been discussed in the literature. Iterated Function System (IFS) is a mathematical scheme to generate fractals. There are several variants of IFSs such as condensation IFS, countable IFS, etc. In this paper

Immunotherapies use components of the patient immune system to selectively target cancer cells. The use of chimeric antigenic receptor (CAR) T cells to treat B-cell malignancies –leukaemias and lymphomas– is one of the most successful examples, with many patients experiencing long-lasting full responses to this therapy. This treatment works by extracting the patient’s T cells and transducing them with

We consider a simple motivating example of a non-Hamiltonian dynamical system with time-dependent constraints obtained by imposing rheonomic non-integrable Bilimovich’s constraint on a freely rotating rigid body. Dynamics of this low-dimensional nonlinear nonautonomous dynamic system involves different kinds of stable and unstable attractors, quasi and strange attractors, compact and noncompact invariant

We borrow the form of potential of the well-known kink-bearing φ4 system in the range between its two vacua and paste it repeatedly into the other ranges to introduce the periodic φ4 system. The paper is devoted to providing a comparative numerical study of the properties of the two systems. Although the two systems are quite similar for a kink (antikink) solution, they usually exhibit different behaviors

Stochastic resonance, found in many natural and engineered bistable systems, refers to a physical phenomenon wherein the response of nonlinear dynamical systems to weak input signal is enhanced by the presence of noise, tuned to the optimal level. However, the observation of this phenomenon for weak subthreshold periodic magnetic field signals in chaotic bistable systems has not been reported. In this

In this paper we analyse the global behaviour of the whole set of ejection orbits in the planar circular RTBP. We consider ejection from the big or the small primary, that is we take the mass parameter μ, the mass traditionally associated with the small primary, in a range of values μ ∈ (0, 1) (the other primary has mass 1−μ). A discussion on the relation between the Lyapunov periodic orbit around

With the development of information technology, the communication between vehicle and vehicle(V2V), vehicle and infrastructure(V2I) promotes traffic efficiency and safety. In this work, we study the mixed traffic with connected and non-connected vehicles, and present the mixed traffic lattice hydrodynamic model. By using linear stability analysis, the stability conditions of the traffic system are

This study investigates a simple model of stage-structured population with density-dependent birth rate. We assume that the breeding season of a population occurs at a certain time of the year, its individuals undergo two stages during their life cycle, and the adjacent generations are nonoverlapping. Reproductive isolation between generations is caused by mature individual death after breeding and

Brucellosis has been increasingly concerned with the animal health and a huge loss of economics. Multiple transmission routes, seasonal pattern and spatial diffusion have been identified in brucellosis propagations. Meanwhile, infectious ability strongly depends on the distance of each adjacent infectious individual. Such property can be captured by a nonlocal infection with some integrable functions

The self-organization of multiple autonomous mobile agents is a trending topic nowadays with applications in robotics, aerospace engineering, and satellite formations. We investigate a model of particles with coupled-oscillators dynamics focusing on the particular case of agents grouping in symmetric clusters while moving in concentric circular trajectories. Our results reveal that certain regions

Stable rotors have been proposed as mechanisms that maintain atrial fibrillation which is the most common arrhythmia worldwide. The information of intracardiac electrograms (EGMs), recorded through multielectrode arrays, is used to characterize the electrical conduction dynamics and thus to identify rotors or reentrant propagating waves. Most of the methods of EGMs processing are based on the assessment

Nestedness refers to a hierarchical organization of complex networks where a given node’s neighbors tend to form a subset of the neighborhoods of higher-degree nodes. Although nestedness has been traditionally interpreted as a macroscopic property that involves all the nodes of the network, recent works have reinterpreted it as a mesoscopic network property, by revealing that interactions in diverse

Given a grayscale, and a positive integer n, how well can we store the image at a compression ratio of n: 1? In this paper we address the above question in extreme cases when n ≫ 50 using “V-variable image compression”.

Efficient and robust synchronization estimation, namely refined cross-sample entropy (RCSE) measure, is presented in this study to analyze complex time series. Unlike the original cross-sample entropy (CSE) that relies on a fixed tolerance r, the proposed RCSE is based on a concept called the cumulative histogram method (CHM) to gain a range of entropy values with different r selections in a certain

In this paper, the combination of Painlevé analysis and symmetry classification is performed on the reaction-diffusion (R–D) types of equations, the Painlevé properties (PPs) and Bäcklund transformations (BTs) are obtained under some conditions. Then, all of the point symmetries of the equations are given by Lie group classification method, moreover, the complete generalized symmetry classifications

In our study, an analytical expression of the second order chirped Pearcey Gaussian vortex beam (CPGVB) in a medium with a parabolic refractive index is derived. We demonstrate its propagation behaviors as well as the effects of the parameters on the propagation properties. Expectedly, the CPGVB performs periodically automatic Fourier transform in the specific positions, but unexpectedly the off-axis

In this paper we use the method of supertracks to study two attractors: the first, called PC8, is generated by Chua’s oscillator and the second is produced by Chua’s circuit equipped with a memristor. In both cases we study in particular the bifurcation maps obtained by varying the control parameters of the circuit one each time and, after applying a discretizing model expressly designed for the purpose

In this paper, an interaction of two-soliton solutions, interactions of the kink with other types of solitary wave solutions of Pavlov equation are constructed via Lie symmetry analysis. The optimal system based on one-dimensional subalgebras of Pavlov equation is computed and used to determine a group of invariant solutions. Furthermore, the Pavlov equation is reduced, with the help of Lie group method

In this paper, we intend to obtain some numerical approximations of inverse problem by means of fractional differential equations under interval uncertainty. For this purpose, using perturbed Collage theorem, we achieve the approximations with the help of minimization procedure. We discuss the Picard operator and the existence with the uniqueness of solutions of interval fractional differential equations

In this paper, a family of arbitrary high order quadratic invariants and energy conservation parametric stochastic partitioned Runge-Kutta methods (SPRK) are constructed for stochastic canonical Hamiltonian systems where the parameters depend on some truncated random variables, step size and numerical solutions. We first apply the P-series and bi-coloured trees theory to analyze the mean-square and

The article investigates the exact and mixed lump wave solitons to the (3+1)-dimensional potential YTSF equation, which is an extension of the Bogoyavlenskii-Schif equation. Different types of interaction solutions in terms of a new merge of positive quadratic functions, trigonometric functions and hyperbolic functions are obtained, which are investigated using the extended three soliton test approach

In this work we start the study of the nodal inverse problem for measure geometric Laplacians in the real line. We analyze the information contained in the set of zeros of eigenfunctions of −Δμ, and we show that it is enough to recover the support of μ. Also, we prove an uniqueness result, and we introduce a method to recover a measure ν absolutely continuous with respect to some measure μ with a continuous

In this paper, we study the determining equations of W-symmetries for backward stochastic differential equations (BSDEs). We have proved that each simple random symmetry of multi-dimensional BSDE can be preserved under simple deterministic change of coordinates. Finally, we study the use of symmetries in studying BSDEs, and find that symmetries of BSDE can not form Lie algebra.

The paper provides a nonlinear stability analysis for a class of stochastic Runge-Kutta methods, applied to problems generating mean-square contractive solutions. In particular, we show how this property is inherited along the solutions generated by the stochastic perturbation of an algebraically stable deterministic Runge-Kutta method. The effectiveness of the results is also confirmed by selected

The paper introduces improved stochastic ϑ-methods for the numerical integration of stochastic Volterra integral equations. Such methods, compared to those introduced by the authors in Conte et al. (2018)[14], have better stability properties. This is here made possible by inheriting the stability properties of the corresponding methods for systems of stochastic differential equations. Such a superiority

This work is devoted to the analysis of a mathematical model of hydropower unit, consisting of synchronous generator, hydraulic turbine, and speed governor. It is motivated by the accident happened on the Sayano-Shushenskaya hydropower plant in 2009. In the analysis we follow the line of classical mathematical control theory approach developed in the works of famous scientists J.C. Maxwell, I.A. Vishnegradsky

Stochastic resonance (SR) in a harmonic oscillator with parametric bounded noise and external periodic force is investigated. By applying the property of bounded noise and using Cameron–Martin formula, infinite chains of linear differential equations are obtained for the spectral amplification, mean-square displacement, and variance. Multiple stochastic resonances are observed for these characteristics

Variants and improvements of the extended Kalman filter (EKF) always encounter a dilemma between the estimation accuracy delivered and the computational burden associated. Targeting to improve this shortcoming, achieving estimations with high accuracy and computational efficiency, this paper investigates a new adaptive high order extended Kalman filter (AHEKF) based on the design of a special order-switching

The classification of problems under uncertainty environments involves the precise description and weighting of fuzzy and random indicators. Although the one-dimensional normal cloud model can effectively handle the fuzziness and randomness of the indicator in an infinite interval, it may ignore the changing tendency of the rating boundary, and become complex with the increment of indicator and sample

Quasiperiodically driven quantum parametric oscillators have been the subject of several recent investigations. Here we show that for such oscillators, the instability zones of the mean position and variance (alternatively the mean energy) for a time developing wave packet are identical for the strongest resonance in the three-dimensional parameter space of the quasiperiodic modulation as it is for

We study two-dimensional (2D) vortex quantum droplets (QDs) trapped by a thicker transverse confinement with a⊥>1μm. Under this circumstance, the Lee-Huang-Yang (LHY) term should be described by its original form in the three-dimensional (3D) configuration. Previous studies have demonstrated that stable 2D vortex QDs can be supported by a thin transverse confinement with a⊥≪1μm. In this case, the LHY

Solitons and cavitons (the latter are localized solutions with singularities) for the nonlocal Whitham equations are studied. The fourth order differential equation for traveling waves with a parameter in front of the fourth derivative is reduced to a reversible Hamiltonian system defined on a two-sheeted four-dimensional space. Solutions of the system which stay on one sheet represent smooth solutions

We formulate a new mathematical model for the Zika infection with mutations and optimal controls. The Zika virus with mutations that cause defects in the newly birth for infected pregnant woman and may lead to further infections in society. Therefore, in the present paper, we utilize this concept into our model and presented a new mathematical model for the characterization of Zika infection with possible

An initial-boundary value problem for the reaction-diffusion Landau–Khalatnikov equation applied to describe polarization switching in ferroelectrics is studied from both theoretical and computational points of view. The existence and uniqueness of a weak solution of the initial-boundary value problem are proved. An absolutely stable monotonic numerical scheme of the second-order accuracy combined

Fractional time quantum mechanics (FTQM) is a method of describing the time evolution of quantum dynamics based on fractional derivatives. For any potential, we obtain the modeling method to describe quantum systems with fractional time consistent with fundamental quantum physics laws, which makes fractional time effects naturally enter quantum mechanics. The method is only using the start states,

In this paper we present a minimal integrated environment-economic growth model. The accumulations of capital and pollution are connected by reciprocal feedbacks. Pollution is an undesirable but inevitable by-product of production, whose efficiency is hindered by pollution. The nexus between pollution and production is embodied in a damage function. The evolution of capital is enriched by the specific

A generalized Duffing oscillator is considered, which takes into account high-order derivatives and power nonlinearities. The Painlevé test is applied to study the integrability of the mathematical model. It is shown that the generalized Duffing oscillator passes the Painlevé test only in the case of the classic Duffing oscillator which is described by the second-order differential equation. However

In this paper, we investigate the influence of the effector-regulatory (Teff-Treg) T cell interaction on the T-cell-mediated autoimmune disease dynamics. The simple 3-dimensional Teff-Treg model is derived from the two-step model reduction of an established 5-dimensional model. The reduced 4- and 3-dimensional models preserve the dynamical behaviors in the original 5-dimensional model, which represents

The present work is devoted to the numerical analysis of the dynamics of a 2D lattice of coupled van der Pol oscillators in the regime of relaxation oscillations. It is shown that the influence of coupling leads to the shift of effective values of the control parameters of individual oscillators. The strong coupling can even cause the transition to bistable dynamics which is never observed in a single

The three-dimensional radial propagation of wave disturbances over a slightly compressible fluid of constant depth is discussed. We focus on resonant triads comprising two gravity modes and one acoustic mode. The derivation of the evolution equations in a non-integral form is made possible by approximating the radial solution by cosine functions in two regions, inner and outer, that are matched at

Self-organization evolution of a population is studied considering generalized reaction-diffusion equations. We proposed a model based on non-local operators that has several of the equations traditionally used in research on population dynamics as particular cases. Then, employing a relatively simple functional form of the non-local kernel, we determined the conditions under which the analyzed population

Cardiac muscle cells can exhibit complex patterns including irregular behaviour such as chaos or (chaotic) early afterdepolarisations (EADs), which can lead to sudden cardiac death. Suitable mathematical models and their analysis help to predict the occurrence of such phenomena and to decode their mechanisms. The focus of this paper is the investigation of dynamics of cardiac muscle cells described

We analyze a two-sector stochastic economic growth model of green transition with pollution externalities and foreign capital. The final good is produced by combining dirty and clean inputs, with different implications on pollution accumulation. Pollution negatively affects production capabilities and can be reduced by switching to the clean input. The clean input is produced by using the dirty input

This paper presents two new non-classical Lagrange basis functions which are based on the new Jacobi-Müntz functions presented by the authors recently. These basis functions are, in fact, generalized forms of the newly generated Jacobi based functions. With respect to these non-classical Lagrange basis functions, two non-classical interpolants are introduced and their error bounds are proved in detail

In this study, the collective and stochastic resonance (SR) behavior of a stochastic nearest neighbor coupled system in a dichotomous fluctuating potential driven by a periodic force are investigated. The exact conditions of stability, synchronization and SR of the system are given analytically and verified by a numerical algorithm. We find that the final dynamic behaviors of the system are the results

This paper focuses on stochastic nutrient-phytoplankton (NP) ecological model under regime switching and complements the findings in [26]. A characterization of the asymptotic behavior of the system under consideration is provided. It is shown that the long-term properties of the NP ecological model can be classified by using a real-valued parameter λ, which can be obtained by solving a system of linear

The process of producing a high-resolution image given a single low-resolution noisy measurement is called single-frame image super-resolution (SISR). Historically, many fractal-based schemes have been proposed in the literature to address the SISR problem. Many conventional interpolation schemes fail to preserve important edge information of natural images and cannot be used blindly for resolution

Phase-locked states with a constant phase shift between the neighboring oscillators are studied in rings of identical Kuramoto oscillators with time-delayed nearest-neighbor coupling. The linear stability of these states is derived and it is found that the stability maps for the dimensionless equations show a high level of symmetry. The size of the attraction basins is numerically investigated. These

We present a case study elaborating on the multiplicity and self-similarity of homoclinic and heteroclinic bifurcation structures in the 2D and 3D parameter spaces of a nonlinear laser model with a Lorenz-like chaotic attractor. In a symbiotic approach combining the traditional parameter continuation methods using MatCont and a newly developed technique called the Deterministic Chaos Prospector (DCP)

Symmetry properties of conservation laws of the (2+1)-dimensional nonlinear Fokker-Planck equation describing the growing cell populations are studied. Firstly, a complete symmetry classification is performed with respect to an equivalence transformation. A two-dimensional optimal system of Lie subalgebras is constructed and used to transform the equations into ordinary differential equations. Secondly

This paper firstly proposes the multiplex oscillatory power network dynamical model, and then investigates the influence of interconnection patterns on synchronous ability of duplex power network being comprised of two subnetworks. In this work, we provide analytical vital conditions for synchronous stability in a multiplex oscillatory power network. Meanwhile, the relationship between interconnection

Collective oscillatory behavior plays a key role in proper functioning of various coupled systems in the real world. However, a variety of damages or deterioration may come up inevitably in coupled systems that can affect macroscopic activity of the entire system. Therefore, we need to provide some remedies to against such aging. To do this, a coupled fractional oscillators model composed of active

Low-dissipation shock-capturing methods usually suffer from various forms of shock instabilities, such as the notorious carbuncle phenomenon, in simulations of hypersonic flows. Many strategies for tackling the shock instability of flux difference splitting schemes, such as HLLC and Roe schemes, have been proposed while little work has been undertaken on the shock instability of flux splitting schemes

The potentially hazardous asteroid is not only the target of planetary defense missions but also an ideal one for scientific exploration of near-Earth objects due to minimal launching budget during its close encounter with Earth. The flyby segment of asteroid shows to be hyperbolic in an Earth-centred inertial frame. To guide the spacecraft captured by the asteroid under the common Earth's gravity

This study presents how the motion, velocity and acceleration of conservative antisymmetric constant force oscillators can be expressed in terms of Jacobi elliptic functions. Two approaches have been developed. In the first approach, one starts from the known period of vibrations and the solution for motion expressed in terms of Jacobi elliptic functions. The second approach is also shown, starting