arXiv subjects

Mustafa Riza

Publications and source records attributed to Mustafa Riza.

10 recordsLinked to original sources

arXiv2025

Dynamic link switching induces stable synchronized states in sparse networks

The flow of information in networked systems composed of multiple interacting elements strongly depends on the level of connectivity among these elements. Sparse connectivity often hinders the emergence of states in which information is globally shared, such as fully synchronized states. In this context, dynamically switching existing network links among system elements can facilitate the onset of synchronization. Here, we address this problem in a double-layer network of FitzHugh-Nagumo oscillators with sparse inter-layer connectivity at fixed density. We show that dynamically switching the existing cross-layer links induces inter-layer synchronization, with a clear dependence on the switching time. In agreement with intuition, shorter switching times suppress large deviations between temporally connected oscillators and more effectively promote synchronization; crucially, this effect persists even when each isolated layer is chaotic. Chaos at the layer level is verified by a strictly positive largest Lyapunov exponent, confirming that synchrony is induced by switching rather than by periodic dynamics. For a minimal double-layer system, we emulate switching using smooth square waves and compute the master stability function (MSF), which is in agreement with direct numerical simulations and delineates the stability regions in parameter space.

nlin.AO↗

arXiv2021

Interlayer Synchronisation of Time-Varying Multiplex Kuramoto--Sakaguchi Networks in the Chimera Regime

We study interlayer synchronisation in a duplex network of $N=300$ nonlocally coupled Kuramoto--Sakaguchi oscillators, with each layer operating in the chimera regime. The interlayer coupling is weak ($\sigma_{12}=0.01$), sparse, and time-varying: a fixed number $N_{IL}$ of replica-node pairs are coupled symmetrically, and the active links are randomly redistributed every $T_{swt}$ time units. We characterise synchronisation by the time-averaged interlayer order parameter $Z$, the master stability function $\Psi(\sigma_{12},T_{swt})$, and the finite-time transverse Lyapunov exponent $\lambda_\perp$. In the static case, full synchronisation ($Z=1$, $\Psi<0$) requires all-to-all interlayer coupling ($N_{IL}=N$). Under temporal switching with $T_{swt}\leq 25$, near-complete synchronisation is achieved with as few as $N_{IL}\approx N/3$ links, while the intralayer chimera structure is preserved. The master stability function confirms that short switching periods render the transverse dynamics stable at link densities where static coupling fails, and the transverse Lyapunov exponent heatmap delineates the critical link number as a joint function of $N_{IL}$ and $T_{swt}$. These results demonstrate that temporal redistribution of sparse interlayer connections can stabilise replica-node coherence in networks with spatially heterogeneous intralayer dynamics.

nlin.AO↗

arXiv2021

Edges of inter-layer synchronization in multilayer networks with time-switching links

We investigate the transition to synchronization in a two-layer network with time-switching inter-layer links. We focus on the role of the number of inter-layer links and the time-scale of topological changes. Initially, we observe a smooth transition to complete synchronization for the static inter-layer topology by increasing the number of inter-layer links. Next, for a dynamic topology with the existent inter-layer links randomly changing among identical units in the layers, we observe a significant improvement in the system synchronizability, i.e., the layers synchronize with lower inter-layer connectivity. More interestingly, we find that, for a critical switching-time, the transition to synchronization occurs abruptly as the number of inter-layer links increases. We interpret this phenomenon as the shrinking, and ultimately, the disappearance of the basin of attraction of a desynchronized network state.

nlin.AO↗

arXiv2021

Energy corrections due to the noncommutative phase-space of the charged isotropic harmonic oscillator in a uniform magnetic field in 3D

In this study, we investigate the effects of noncommutative Quantum Mechanics in three dimensions on the energy levels of a charged isotropic harmonic oscillator in the presence of a uniform magnetic field in the z-direction. The extension of this problem to three dimensions proves to be non-trivial. We obtain the first-order corrections to the energy-levels in closed form in the low energy limit of weak noncommutativity. The most important result we can note is that all energy corrections due to noncommutativity are negative and their magnitude increase with increasing Quantum numbers and magnetic field.

quant-ph↗

arXiv2021

Energy corrections due to the Non-commutative Phase-Space of the Charged Harmonic Oscillator in a constant magnetic field in 3D

quant-ph↗

arXiv2015

A Modified Quadratic Lorenz attractor

This study introduces a modified quadratic Lorenz attractor. The properties of this new chaotic system are analysed and discussed in detail, by determining the equilibria points, the eigenvalues of the Jacobian, and the Lyapunov exponents. The numerical simulations, the time series analysis, and the projections to the $xy$-plane, $xz$-plane, and $yz$-plane are conducted to highlight the chaotic behaviour. The multiplicative form of the new system is also presented and the simulations are conducted using multiplicative Runge-Kutta methods.

math.DS↗

arXiv2015

Bigeometric Calculus and Runge Kutta Method

The properties of the Bigeometric or proportional derivative are presented and discussed explicitly. Based on this derivative, the Bigeometric Taylor theorem is worked out. As an application of this calculus, the Bigeometric Runge-Kutta method is derived and is applied to academic examples, with known closed form solutions, and a sample problem from mathematical modelling in biology. The comparison of the results of the Bigeometric Runge-Kutta method with the ordinary Runge-Kutta method shows that the Bigeometric Runge-Kutta method is at least for a particular set of initial value problems superior with respect to accuracy and computation time to the ordinary Runge-Kutta method.

math.GM↗

arXiv2013

The Runge-Kutta Method in Geometric Multiplicative Calculus

This paper illuminates the derivation, the applicability, and the efficiency of the Multiplicative Runge-Kutta Method, derived in the frame- work of geometric multiplicative calculus. The removal of the restrictions of geometric multiplicative calculus to positive-valued functions of real variable and the fact that the multiplicative derivative does not exist at the roots of the function, is presented explicitly to ensure that the proposed method is uni- versally applicable. The error analysis is also carried out in the framework of geometric multiplicative calculus explicitly. The presented method is applied to various problems and the results are compared to the ones obtained from the Ordinary Runge-Kutta Method. Moreover, for one example, a comparison of the computation time vs. relative error, is worked out, to illustrate the general advantage of the proposed method.

math.NA↗

arXiv2013

On Complex Multiplicative Integration

In the present paper we extend the multiplicative integral to complex-valued functions of complex variable. The main difficulty in this way, that is the multi-valued nature of the complex logarithm, is avoided by division of the interval of integration to a finite number of local intervals, in each of which the complex logarithm can be localized in one of its branches. Interestingly, the complex multiplicative integral became a multi-valued function. Some basic properties of this integral are considered. In particular, it is proved that this integral and the complex multiplicative derivative bonded in a kind of fundamental theorem.

math.CV↗

arXiv2011

Complex Multiplicative Calculus

In the present paper we extend the concepts of multiplicative de- rivative and integral to complex-valued functions of complex variable. Some drawbacks, arising with these concepts in the real case, are explained satis- factorily. Properties of complex multiplicative derivatives and integrals are studied. In particular, the fundamental theorem of complex multiplicative calculus, relating these concepts, is proved. It is shown that complex multi- plicative calculus is not just another realization of the ordinary calculus. In particular, the Cauchy formula of complex calculus disappears in multiplicative complex calculus.

math.CV↗