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Construction of Planar Vector Fields with a Nonsimple Critical Point of Prescribed Topological Structure
The problem of constructing n -linear ( n ≥ 2) plane vector fields with an isolated critical point and given separatrices of prescribed types is...
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Stability and Turing Patterns of a Predator-prey Model with Holling Type II Functional Response and Allee Effect in Predator
In this paper, we are concerned with a predator-prey model with Holling type II functional response and Allee effect in predator. We first...
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Dynamical Models of Interrelation in a Class of Artificial Networks
The system of ordinary differential equations that models a type of artificial networks is considered. The system consists of a sigmoidal function...
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Topaj–Pikovsky Involution in the Hamiltonian Lattice of Locally Coupled Oscillators
We discuss the Hamiltonian model of an oscillator lattice with local coupling. The Hamiltonian model describes localized spatial modes of nonlinear...
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Modelling Atwood’s Machine with Three Degrees of Freedom
A generalized model of the Atwood machine when two bodies can swing in a plane is considered. Combining symbolic and numerical calculations, we have...
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Reliable Numerical Modelling of Malaria Propagation
We investigate biological processes, particularly the propagation of malaria. Both the continuous and the numerical models on some fixed mesh should...
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Comparing Dynamics Initiated by an Attached Oscillating Particle for the Nonholonomic Model of a Chaplygin Sleigh and for a Model with Strong Transverse and Weak Longitudinal Viscous Friction Applied at a Fixed Point on the Body
This paper addresses the problem of a rigid body moving on a plane (a platform) whose motion is initiated by oscillations of a point mass relative to...
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Theoretical analyses on bed topography responses in large depth-to-width ratio river bends with constant curvatures
Bed morphology is the result of a dynamic response to a complex meandering river system. It is an important factor for the further development of...
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Regular and Chaotic Dynamics of a Chaplygin Sleigh due to Periodic Switch of the Nonholonomic Constraint
The main goal of the article is to suggest a two-dimensional map that could play the role of a generalized model similar to the standard...
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Analysis and Optimal Control of an Intracellular Delayed HIV Model with CTL Immune Response
A delayed model describing the dynamics of Human Immunodeficiency Virus (HIV) with Cytotoxic T Lymphocytes (CTL) immune response is investigated. The...
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Motion of a Swinging Atwood’s Machine: Simulation and Analysis with Mathematica
A generalized model of the Atwood machine when one body is constrained to move along a vertical axis while the other one can swing in a plane is...
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Fractional-step θ-method for solving singularly perturbed problem in ecology
We consider a predator-prey model arising in ecology that describes a slow-fast dynamical system. The dynamics of the model is expressed by a system...
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Regular and chaotic motions of a Chaplygin sleigh under periodic pulsed torque impacts
For a Chaplygin sleigh on a plane, which is a paradigmatic system of nonholonomic mechanics, we consider dynamics driven by periodic pulses of...
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Environmentally induced amplitude death and firing provocation in large-scale networks of neuronal systems
We study the dynamics of multielement neuronal systems taking into account both the direct interaction between the cells via linear coupling and...
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A mathematical model of the photosynthetic carbon metabolism has multiple steady states under the same parameter conditions
This paper analyzes a mathematical model of the photosynthetic carbon metabolism, which incorporates not only the Calvin-Benson cycle, but also...
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The role of normally hyperbolic invariant manifolds (NHIMS) in the context of the phase space setting for chemical reaction dynamics
In this paper we give an introduction to the notion of a normally hyperbolic invariant manifold (NHIM) and its role in chemical reaction dynamics.We...
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Theoretical analyses on hydrodynamic instability in narrow deep river with variable curvature
Bending river is the most common river type in nature, and it is also a typical example for river evolution. The transform of the flow pattern can...
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No periodic orbits for the type A Bianchi’s systems
It is known that the 6 models of Bianchi class A have no periodic solutions. In this article we provide a new, direct, unified and easier proof of...
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Symmetric Hopf bifurcation in implicit neutral functional differential equations: Equivariant degree approach
In this paper, we develop a general framework for studying symmetric Hopf bifurcation phenomenon for (symmetric) implicit neutral functional...
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Outbreak analysis of an SIS epidemic model with rewiring
This paper is devoted to the analysis of the early dynamics of an SIS epidemic model defined on networks. The model, introduced by Gross et al. (Phys...