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Yayın New criteria for the existence of stable equilibrium points in nonsymmetric cellular neural networks(IEEE, 2003) Özcan, Neyir; Arık, Sabri; Tavşanoğlu, Ahmet VedatA new criteria for the existence of stable equilibrium points in nonsymmetric cellular neural networks (CNN) was presented. It was shown that the results obtained can be used to derive some complete stability conditions for some special classes of CNNs such as positive cell-linking CNNs, opposite-sign CNNs and dominant-template CNNs. The model of the CNN whose dynamical behavior was described by the state equations was discussed.Yayın Breaking an orbit-based symmetric cryptosystem(Pergamon-Elsevier Science Ltd, 2011-09) Solak, Ercan; Rhouma, Rhouma; Belghith, Safya MdimeghWe report a break for a recently proposed class of cryptosystems. The cryptosystem uses constant points of a periodic secret orbit to encrypt the plaintext. In order to break the system, it suffices to sort the constant points and find the initial fixed point. We also report breaks for modified versions of the cryptosystem. In addition, we discuss some efficiency issues of the cryptosystem.Yayın Normal forms and nonlocal chaotic behavior in Sprott systems(Pergamon-Elsevier Science, 2003-06) Perdahçı, Nazım Ziya; Hacınlıyan, Avadis SimonThe Sprott systems are used as benchmarks for investigating the applicability of the normal form transformation in estimating nonlocal properties of attractors such as positive and zero Liapunov exponents. Possibility of a relation between complex conjugate eigenvalue pairs and zero Liapunov exponents; conditions under which the normal form expansion can represent the attractor; an averaging relation for the largest Liapunov exponent based on this representation are studied. Nonlinear transformations that can change the order of a resonance are considered. In spite of their convergence problems, it is seen that the normal form approach can give reasonable estimates of nonlocal properties of attractors near Hopf bifurcations.Yayın The statistics of energy states of a Hookean model for proteins(TÜBİTAK, 2000) Erzan, Ayşe; Tüzel, ErkanA generic model of a random polypeptide chain, with discrete torsional degrees of freedom and Hookean springs connecting pairs of hydrophobia residues, reproduces the energy probability distribution of real proteins over a very large range of energies. We show that this system with harmonic interactions, under dissipative dynamics driven by random noise, leads to a distribution of energy states obeying a modified one-dimensional Ornstein-Uhlenbeck process with reflecting boundary conditions, and giving rise to distributions of the Wigner or inverse Gaussian form. A continuum approximation leads to a path integral formulation of the problem.Yayın Kaotik kriptografinin çilesi(IEEE, 2013-06-13) Solak, ErcanSon yirmi yıldır araştırılan bir konu olmasına rağmen, kaotik kriptografi ana akım kriptografi literatüründe yer almıyor. Bu makalede, bu ayrımın nedenleri üzerinde durulmuştur.Yayın Cryptanalysis of image encryption with compound chaotic sequence(IEEE, 2009) Solak, ErcanRecently, an image encryption algorithm based on compound chaotic sequence was proposed [Tong et al., Image and Vision Computing 26 (2008) 843]. In this paper, we analyze the security weaknesses of the proposal. We give chosen-plaintext and known-plaintext attacks that yield the secret parameters of the algoritm. Our simulation results show that the computational complexity of the attacks is quite low.
