23 papers · ranked by Valyu relevance
Xingyuan Wang, Nana Guan, Hongyu Zhao, Siwei Wang + 1 more
As a kind of spatiotemporal chaos, coupled map lattice (CML) is widely applied into image encryption because of its advantages of more complex dynamical behavior and lower computational overhead. Firstly, this paper proposed a novel spatiotemporal chaos model (MCML) by mixing Logistic, Sine and Tent maps into CML map…
Joydeep Singha, Neelima Gupte
We study the existence of chimera states, i.e. mixed states, in a globally coupled sine circle map lattice, with different strengths of inter-group and intra-group coupling. We find that at specific values of the parameters of the CML, a completely random initial condition evolves to chimera states, having a phase…
Warambhe, Manoj C., Gade, Prashant M.
- We define an order parameter for zigzag and checkerboard patterns on a discrete lattice. - We find that the order parameter shows a power-law decay over a range of parameter values and not just critical point. - We define persistence in these systems and it shows power-law decay in the same range with exponents…
Davide Faranda, Hamza Ghoudi, Pierre Guiraud, Sandro Vaienti
We show that the probability of the appearance of synchronization in chaotic coupled map lattices is related to the distribution of the maximum of a certain observable evaluated along almost all orbits. We show that such a distribution belongs to the family of extreme value laws, whose parameters, namely the extremal…
Timothy Killingback, Gregory Loftus, Bala Sundaram
Spatial pattern formation is a key feature of many natural systems in physics, chemistry and biology. The essential theoretical issue in understanding pattern formation is to explain how a spatially homogeneous initial state can undergo spontaneous symmetry breaking leading to a stable spatial pattern. This problem is…
P. Palaniyandi, Govindan Rangarajan
We propose a mathematical model for storage and recall of images using coupled maps. We start by theoretically investigating targeted synchronization in coupled map systems wherein only a desired (partial) subset of the maps is made to synchronize. A simple method is introduced to specify coupling coefficients such…
Rubén Berenguel, Ernest Fontich
In this paper we present local Sternberg conjugation theorems near attracting fixed points for lattice systems. The interactions are spatially decaying and are not restricted to finite distance. The conjugations obtained retain the same spatial decay. In the presence of resonances the conjugations are to a polynomial…
Li Xu, Guang Zhang, Haoyue Cui, Gui-Quan Sun
The logistic coupled map lattices (LCML) have been widely investigated as well as their pattern dynamics. The patterns formation may depend on not only fluctuations of system parameters, but variation of the initial conditions. However, the mathematical discussion is quite few for the effect of initial values so far.…
Joydeep Singha, Neelima Gupte
We study the existence of chimera states, i.e. mixed states, in a globally coupled sine circle map lattice, with different strengths of inter-group and intra-group coupling. We find that at specific values of the parameters of the CML, a completely random initial condition evolves to chimera states, having a phase…
Jin Yan, Christian Beck, Airton Deppman, Bíró Tamás Sándor
Recent mathematical investigations have shown that under very general conditions, exponential mixing implies the Bernoulli property. As a concrete example of statistical mechanics that are exponentially mixing we consider the Bernoulli shift dynamics by Chebyshev maps of arbitrary order $N\geq2$, which maximizes…
Mauricio Girardi-Schappo, Marcelo HR Tragtenberg, Osame Kinouchi
To study neurons with computational tools, one may call upon, at least, two different approaches: (i) Hodgkin-Huxley like neurons [1] (i.e. biological neurons) and (ii) formal neurons (e.g. Hindmarsh-Rose (HR) model [2], Kinouchi-Tragtenberg (KT) model [3], etc). Formal neurons may be represented by ordinary…
Marcelo O. Magnasco, Stuart A. Kauffman, Roberto Serra, Ilya Shmulevich + 1 more
'Ilya Shmulevich' 'Sui Huang'] In theoretical biology, robustness refers to the ability of a biological system to function properly even under perturbation of basic parameters (e.g., temperature or pH), which in mathematical models is reflected in not needing to fine-tune basic parameter constants; flexibility refers…
Hans Muller Mendonca, Ralf Tönjes, Tiago Pereira, Andrea Rapisarda
We study the transition to synchronization in large, dense networks of chaotic circle maps, where an exact solution of the mean-field dynamics in the infinite network and all-to-all coupling limit is known. In dense networks of finite size and link probability of smaller than one, the incoherent state is meta-stable…
Kaushik Roy, Paul François
The ‘segmentation clock’ is an emergent embryonic oscillator that controls the periodic formation of vertebrae precursors (or somites). It relies on the self-organization at the Pre Somitic Mesoderm (PSM) level of multiple coupled cellular oscillators. Dissociation-reaggregation experiments have further revealed that…
Authors not listed
We present a coupled-oscillator toy model that describes the low-frequency lattice-like vibrations observed in Raman and inelastic neutron scattering spectra of β-sheet structures found in amyloid fibrils. In this model, the strands of the fibril β-sheet structures are treated as harmonically oscillating rods with…
Sophia R. Sklan, Baowen Li
In most systems, its division into interacting constituent elements gives rise to a natural network structure. Analyzing the dynamics of these elements and the topology of these natural graphs gave rise to the fields of (nonlinear) dynamics and network science, respectively. However, just as an object in a potential…
Annabel Large, Ian Holmes
We investigate the use of Expectation–Maximization (em) and variational Bayes for inferring rates and interactions under models of molecular coevolution. We first review em theory for continuous-time Markov chains (ctmcs) and develop it for coevolutionary models, exploiting exchangeability and reversibility symmetries…
Lisa Willis, Alexandre Kabla
The combination of laterally activating and inhibiting feedbacks is well known to spontaneously generate spatial organisation. It was introduced by Gierer and Meinhardt as an extension of Turing’s great insight, that two reacting and diffusing chemicals can spontaneously drive spatial morphogenesis per se. In this…
Basant Lal Sharma
A family of solitary waves is constructed in Frenkel-Kontorova model and its continuum and quasicontinuum approximations. Each solitary waves is characterised by the number of local maxima in its profile and a relation between external force and the velocity of wave. Such waves may be interpreted as a coherent motion…
Authors not listed
Finite-temperature lattice free energy differences between polymorphs of molecular crystals are fundamental to understanding and predicting the relative stability relationships underpinning polymorphism, yet are computationally expensive to obtain. Here, we implement and critically assess machine-learning-enabled…
Gustavo Deco, Yonatan Sanz Perl, Natasha Greenstein, Shamil Chandaria + 2 more
Emerging new research indicates evidence of quantum-like (QL) probability laws, including interference effects, in non-quantum physical systems using coupled oscillators. This can produce QL states which can compute in a QL fashion. Given the success of using coupled oscillators for human whole-brain modelling, we…
Qichen Huang, Haoyang Guo
Cellular automata and graph reaction–diffusion systems encode local spatial interactions in different mathematical forms. We develop a cochain-operator calculus for these two settings. Over a finite field F_q_, every local rule on a finite neighborhood has a unique reduced polynomial representative. On an oriented…
Simon Adriano Munoz Lagunas, Jeehye An, Leon Stefanovski, Petra Ritter
Computational neuroscience offers powerful tools for understanding brain function in both healthy and diseased states. However, detailed data on microscale mechanisms—such as those involved in genetics and pharmacology—are often derived from mouse experiments and further lack integration into whole-brain models. In…