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article

Stabilizing constrained chaotic system using a symplectic psuedospectral method

H. Peng, X. Wang, B. Shi, S. Zhang, more

Communications in Nonlinear Science and Numerical Simulation > 2018 > 56 > Complete > 77-92

The problem of controlling chaotic systems has drawn much attention in the last two decades. However, the controlled system may be subjected to complicated constraints and few researches on controlling chaos take constraints into consideration. Therefore, the stabilization of constrained chaotic system is solved under the frame of nonlinear optimal control in this paper. A symplectic pseudospectral...

article

Generative complexity of Gray-Scott model

A. Adamatzky

Communications in Nonlinear Science and Numerical Simulation > 2018 > 56 > Complete > 457-466

In the Gray-Scott reaction-diffusion system one reactant is constantly fed in the system, another reactant is reproduced by consuming the supplied reactant and also converted to an inert product. The rate of feeding one reactant in the system and the rate of removing another reactant from the system determine configurations of concentration profiles: stripes, spots, waves. We calculate the generative...

article

K(m, n) equations with fifth order symmetries and their integrability

K. Tian

Communications in Nonlinear Science and Numerical Simulation > 2018 > 56 > Complete > 490-498

For K(m, n) equation u_t=D_x³(uⁿ)+αD_x(u^m), all non-degenerate (n <> 0) cases admitting fifth order symmetries are identified, including K(m₁, 1), K(m₂,-1/2) and K(m₃,-2), where m₁=0,1,2,3,m₂=-1/2,0,1,3/2 and m₃=-2,-1,0,1. For five less studied cases, namely K(0,-2),K(-1,-2),K(-2,-2),K(-1/2,-1/2) and K(3/2,-1/2), bi-Hamiltonian structures are established through their invertible links with some...

article

Seamless variation of isometric and anisometric dynamical integrity measures in basins's erosion

P. Belardinelli, S. Lenci, G. Rega

Communications in Nonlinear Science and Numerical Simulation > 2018 > 56 > Complete > 499-507

Anisometric integrity measures defined as improvement and generalization of two existing measures (LIM, local integrity measure, and IF, integrity factor) of the extent and compactness of basins of attraction are introduced. Non-equidistant measures make it possible to account for inhomogeneous sensitivities of the state space variables to perturbations, thus permitting a more confident and targeted...

article

The interaction between predator strategy and prey competition in a pair of multi-predator multi-prey lattices

G.M. Abernethy, M. McCartney, D.H. Glass

Communications in Nonlinear Science and Numerical Simulation > 2018 > 56 > Complete > 9-33

A computational study of a system of ten prey phenotypes and either one or ten predator phenotypes with a range of foraging behaviours, arranged on two separate one-dimensional lattices, is presented. Mutation between nearest neighbours along the prey lattice occurs at a constant rate, and mutation may or may not be enabled for the predators. The significance of competition amongst the prey is investigated...

article

A Class of time-fractional hemivariational inequalities with application to frictional contact problem

S. Zeng, S. Migorski

Communications in Nonlinear Science and Numerical Simulation > 2018 > 56 > Complete > 34-48

In this paper a class of elliptic hemivariational inequalities involving the time-fractional order integral operator is investigated. Exploiting the Rothe method and using the surjectivity of multivalued pseudomonotone operators, a result on existence of solution to the problem is established. Then, this abstract result is applied to provide a theorem on the weak solvability of a fractional viscoelastic...

article

A novel analytic approximation method with a convergence acceleration parameter for solving nonlinear problems

X. Zhang, L. Zou, S. Liang, C. Liu

Communications in Nonlinear Science and Numerical Simulation > 2018 > 56 > Complete > 354-364

In this paper, a new analytic approximation method with a convergence acceleration parameter c is first proposed. The parameter c is used to adjust and control the convergence region and rate of the resulting series solution. It turns out that the convergence region and rate can be greatly enlarged by choosing a proper value of c. Furthermore, a numerical approach for finding the optimal value of...

article

Convergence regions for the Chebyshev-Halley family

B. Campos, J. Canela, P. Vindel

Communications in Nonlinear Science and Numerical Simulation > 2018 > 56 > Complete > 508-525

In this paper we study the dynamical behavior of the Chebyshev-Halley methods on the family of degree n polynomials zⁿ+c. We prove that, despite increasing the degree, it is still possible to draw the parameter space by using the orbit of a single critical point. For the methods having z=~ as an attracting fixed point, we show how the basins of attraction of the roots become smaller as the value of...

article

Predicting seizure by modeling synaptic plasticity based on EEG signals - a case study of inherited epilepsy

H. Zhang, J. Su, Q. Wang, Y. Liu, more

Communications in Nonlinear Science and Numerical Simulation > 2018 > 56 > Complete > 330-343

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...

article

Mode locking and quasiperiodicity in a discrete-time Chialvo neuron model

F. Wang, H. Cao

Communications in Nonlinear Science and Numerical Simulation > 2018 > 56 > Complete > 481-489

The two-dimensional parameter spaces of a discrete-time Chialvo neuron model are investigated. Our studies demonstrate that for all our choice of two parameters (i) the fixed point is destabilized via Neimark-Sacker bifurcation; (ii) there exist mode locking structures like Arnold tongues and shrimps, with periods organized in a Farey tree sequence, embedded in quasiperiodic/chaotic region. We determine...

article

Experimental evidence of chaos synchronization via cyclic coupling

A.I. Egunjobi, O.I. Olusola, A.N. Njah, S. Saha, more

Communications in Nonlinear Science and Numerical Simulation > 2018 > 56 > Complete > 588-595

In this paper, we implement, in electronic experiment, a type of cyclic coupling to realize synchronization between two identical chaotic oscillators. In cyclic coupling, the oscillators exchange energy or information between each other via two different pairs of state variables. As a consequence, synchronization is found enhanced by the application of cyclic coupling to a selected set of variables...

article

Periodic or chaotic bursting dynamics via delayed pitchfork bifurcation in a slow-varying controlled system

Y. Yu, Z. Zhang, X. Han

Communications in Nonlinear Science and Numerical Simulation > 2018 > 56 > Complete > 380-391

In this work, we aim to demonstrate the novel routes to periodic and chaotic bursting, i.e., the different bursting dynamics via delayed pitchfork bifurcations around stable attractors, in the classical controlled Lu system. First, by computing the corresponding characteristic polynomial, we determine where some critical values about bifurcation behaviors appear in the Lu system. Moreover, the transition...

article

Stochastic differential calculus for Gaussian and non-Gaussian noises: A critical review

G. Falsone

Communications in Nonlinear Science and Numerical Simulation > 2018 > 56 > Complete > 198-216

In this paper a review of the literature works devoted to the study of stochastic differential equations (SDEs) subjected to Gaussian and non-Gaussian white noises and to fractional Brownian noises is given. In these cases, particular attention must be paid in treating the SDEs because the classical rules of the differential calculus, as the Newton-Leibnitz one, cannot be applied or are applicable...

article

The Prabhakar or three parameter Mittag-Leffler function: Theory and application

R. Garra, R. Garrappa

Communications in Nonlinear Science and Numerical Simulation > 2018 > 56 > Complete > 314-329

The Prabhakar function (namely, a three parameter Mittag-Leffler function) is investigated. This function plays a fundamental role in the description of the anomalous dielectric properties in disordered materials and heterogeneous systems manifesting simultaneous nonlocality and nonlinearity and, more generally, in models of Havriliak-Negami type. After reviewing some of the main properties of the...

article

Resonant interaction of φ⁴ kink with PT-symmetric perturbation with spatially periodic gain/loss coefficient

D. Saadatmand, D.I. Borisov, P.G. Kevrekidis, K. Zhou, more

Communications in Nonlinear Science and Numerical Simulation > 2018 > 56 > Complete > 62-76

The resonant interaction of the φ⁴ kink with a PT-symmetric perturbation is observed in the numerical study performed in the frame of the continuum model and with the help of a two degree of freedom collective variable model derived in PRA 89, 010102(R). The perturbation is in the form of first partial derivative in time term with a spatially periodic gain/loss coefficient. When the kink interacts...

article

A non-local structural derivative model for characterization of ultraslow diffusion in dense colloids

Y. Liang, W. Chen

Communications in Nonlinear Science and Numerical Simulation > 2018 > 56 > Complete > 131-137

Ultraslow diffusion has been observed in numerous complicated systems. Its mean squared displacement (MSD) is not a power law function of time, but instead a logarithmic function, and in some cases grows even more slowly than the logarithmic rate. The distributed-order fractional diffusion equation model simply does not work for the general ultraslow diffusion. Recent study has used the local structural...

article

Modeling malware propagation using a carrier compartment

J.D. Hernandez Guillen, A. Martin del Rey

Communications in Nonlinear Science and Numerical Simulation > 2018 > 56 > Complete > 217-226

The great majority of mathematical models proposed to simulate malware spreading are based on systems of ordinary differential equations. These are compartmental models where the devices are classified according to some types: susceptible, exposed, infectious, recovered, etc. As far as we know, there is not any model considering the special class of carrier devices. This type is constituted by the...

article

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Communications in Nonlinear Science and Numerical Simulation > 2018 > 56 > Complete > IFC

article

Autonomous choices among deterministic evolution-laws as source of uncertainty

L. Trujillo, A. Meyroneinc, K. Campos, O. Rendon, more

Communications in Nonlinear Science and Numerical Simulation > 2018 > 56 > Complete > 405-418

We provide evidence of an extreme form of sensitivity to initial conditions in a family of one-dimensional self-ruling dynamical systems. We prove that some hyperchaotic sequences are closed-form expressions of the orbits of these pseudo-random dynamical systems. Each chaotic system in this family exhibits a sensitivity to initial conditions that encompasses the sequence of choices of the evolution...

article

Chimera states in nonlocally coupled phase oscillators with biharmonic interaction

H. Cheng, Q. Dai, N. Wu, Y. Feng, more

Communications in Nonlinear Science and Numerical Simulation > 2018 > 56 > Complete > 1-8

Chimera states, which consist of coexisting domains of coherent and incoherent parts, have been observed in a variety of systems. Most of previous works on chimera states have taken into account specific form of interaction between oscillators, for example, sinusoidal coupling or diffusive coupling. Here, we investigate chimera dynamics in nonlocally coupled phase oscillators with biharmonic interaction...

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Stabilizing constrained chaotic system using a symplectic psuedospectral method

Generative complexity of Gray-Scott model

K(m, n) equations with fifth order symmetries and their integrability

Seamless variation of isometric and anisometric dynamical integrity measures in basins's erosion

The interaction between predator strategy and prey competition in a pair of multi-predator multi-prey lattices

A Class of time-fractional hemivariational inequalities with application to frictional contact problem

A novel analytic approximation method with a convergence acceleration parameter for solving nonlinear problems

Convergence regions for the Chebyshev-Halley family

Predicting seizure by modeling synaptic plasticity based on EEG signals - a case study of inherited epilepsy

Mode locking and quasiperiodicity in a discrete-time Chialvo neuron model

Experimental evidence of chaos synchronization via cyclic coupling

Periodic or chaotic bursting dynamics via delayed pitchfork bifurcation in a slow-varying controlled system

Stochastic differential calculus for Gaussian and non-Gaussian noises: A critical review

The Prabhakar or three parameter Mittag-Leffler function: Theory and application

Resonant interaction of φ⁴ kink with PT-symmetric perturbation with spatially periodic gain/loss coefficient

A non-local structural derivative model for characterization of ultraslow diffusion in dense colloids

Modeling malware propagation using a carrier compartment

Editors

Autonomous choices among deterministic evolution-laws as source of uncertainty

Chimera states in nonlocally coupled phase oscillators with biharmonic interaction

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